An amplifier will just
amplify the signal coming out of the analogue headphone output of the mobile phone. Some have line out mode but that's basically just running it at full volume and you just get less distortion and noise because of the very high impedance of the amplifier's input circuit.
A DAC will take the digital signal from the phone completely bypassing everything in it except for the CPU and any software DSP running (note that not all of Samsung's built in DSP features will work via USB output). It will then spit out an analogue line signal, but you still need to amplify that into a signal that will move a transducer properly. Even if such a transducer doesn't need more than 1.5V to destroy your eardrums, a DAC's output system will not be able to cope with the curent requirements if it's a low impedance headphone (that gets worse with low sensitivity headphones, but then again that's why I gave the 1.5V part).
What you have been referring to are DAC-HPamps, which have both the DAC circuit
and a headphone amplifier circuit built into the same device. The difference is still the same - either you let the phone's audio chip run as both a DAC and analogue output chip - ie, think of how most mobile CPUs also have a GPU chip in the same module - and feed the amplifier an analogue signal, which
might have some noise or non-linear response, or just use a DAC-HPamp and leave everything audio save for the DSP to the external, audio-specific device, in which case, some phones
might not work with some devices. Or it works that it sends a signal, but it can still have noise.
So basically there's a risk that either way there's a probability that it won't work, either the amp picks up a crap signal, or your phone isn't compatible. It's hard to say which one is more likely other than if you can check on the Android DACs thread that your particular phone works with USB OTG audio, and generally flagship phones tend to have good audio output on their own (just not enough power for most headphones and a few oddball IEMs) while also supporting USB audio via USB OTG. If you have an iPhone, the same is pretty much true, although (just switch over OTG and 3.5mm to "appropriate dongle") there's less variance to troll through since every year there's really just one version every year (well, more than one, but audio functionality is consistent anyway).
In short: we can't give specific answers unless it's somebody with the exact specific same version as your phone. That's not just USB audio functionality but also sound quality of the analogue output, because some phones have alternate audio chips. Samsung makes Snapdragon versions for T-Mobile, and while they're not bad on their own, some Galaxy S versions suck compared to the Exynos+Wolfson versions of the same phones. My S3 had bloated bass regardless of whether you plug in a 16ohm or 32ohm IEM, or even if you feed the signal into a 1000ohm amplifier input stage.
As to how important they are, that also varies. Regardless of the system, all systems have a circuit or single chip that serves as a DAC and amplifier, which in the case of mobile phones is a single integrated audio chips (which on Snapdragon CPUs is built into the CPU itself, in some cases the performance is handicapped to favor battery life like how you
That depends on a lot of variables. Many flagship smartphones and next tier down (or different design/market, parallel lines, like the Sx and Note x, Gx and Vx0, etc) can do well enough on a 100dB/1mW sensitivity IEM that in only rare cases (like some Snapdragon Galaxy S phones) will you find some problem with the power (S3 Snapdragon has bloated bass) or noise; go a few tiers down and you'll find that problem more consistent across more smartphones (some old HTC my brother had, his old LG Stylo, my J7 Prime, my cousin's J7 Pro, etc). LG's G6 and V20 and up tend to be the best out there though, right up there with iPhones (if you can live with dongles; although technically the dongle reliant models have their own audio chips built into the dongles).
So in other words it depends on your phone and what IEM you're using. If you're using for example a Galaxy Note 8 or S9, and more so if you have the Exynos+Wolfson versions (more of the S9 probably; never had a problem on all of the Notes) and an IEM with an impedance of around ~32ohms (maybe down to 16phms on the Exynos+Wolfson versions) to ~120ohms and sensitivity of around 105dB/1mW, then an external device is probably not going to have any appreciable difference outside of using it on a desk where 1) you're doing more critical listening, ie, your attention isn't divided, and 2) the noisefloor is also lower, for the effort to lug something strapped on to the phone which you will end up bringing up to your mouth when a call comes in because even if your IEM has a mic, it won't go through DAC-HPamps which have no mic preamp inputs (much less an ADC).
He did (partially) answer what you asked...
...but he can't answer beyond that because, surprise, he's only really used the digital output on the few Androids he has owned, while iPhones have very few models and have generally had consistent audio output driving IEMs directly since the iP5. At the same time, read back what I've been saying on this thread. Not getting a direct answer to a not even specific enough question isn't "not answering" (sic) your question, we're saying 1) we can't give a very specific answer and nobody can unless they have the very specific phone version and IEM in question (something I also already said above) and 2) no one can even begin to do so when nobody knows what phone and IEM (or headphone) you are using.
That's like asking "do I need a turbocharger or supercharger?" without stating what your car and your engine is and what you're going to use it for. If you already have an American car with a 7.0L V8 then probably not, unless you want to go into higher tiers of drag racing events; if you have anything else with a smaller engine, a high revving Honda typically would not work with well with the strong, pulsing waves of intake air from a screw-type blower, and requires either a turbo (which used to spool up slowly, especially with a smaller engine) or a centrifugal supercharger (which, like a screw-type, has parasitic drivetrain loss), but a lower revving Toyota engine can work with a screw-type supercharger the same way some Mercedes with long stroke engines also use them, from the four banger on the old SLK and C-Class all the way to the xx55 AMG models; then how much boost is needed or where depends on whether you just want to easily get past long, slow trucks before slamming into incoming traffic, or if you want a lot of power all the way to redline for the track but improve the low end for tight corners, or just not give a hoot about torque below 3000rpm because you're going to drag race anyway.
In the same manner, if you're using for example a Galaxy Note 8 or S9, and more so if you have the Exynos+Wolfson versions (more of the S9 probably; never had a problem on all of the Notes) and an IEM with an impedance of around ~32ohms (maybe down to 16phms on the Exynos+Wolfson versions) to ~120ohms and sensitivity of around 105dB/1mW, then an external device is probably not going to have any appreciable difference outside of using it on a desk where 1) you're doing more critical listening, ie, your attention isn't divided, and 2) the noisefloor is also lower, for the effort to lug something strapped on to the phone which you will end up bringing up to your mouth when a call comes in because even if your IEM has a mic, it won't go through DAC-HPamps which have no mic preamp inputs (much less an ADC).
What IEM and what phone are you using? If you're using for example a Galaxy Note 8 or S9, and more so if you have the Exynos+Wolfson versions (more of the S9 probably; never had a problem on all of the Notes) and an IEM with an impedance of around ~32ohms (maybe down to 16phms on the Exynos+Wolfson versions) to ~120ohms and sensitivity of around 105dB/1mW, then an external device is probably not going to have any appreciable difference outside of using it on a desk where 1) you're doing more critical listening, ie, your attention isn't divided, and 2) the noisefloor is also lower, for the effort to lug something strapped on to the phone which you will end up bringing up to your mouth when a call comes in because even if your IEM has a mic, it won't go through DAC-HPamps which have no mic preamp inputs (much less an ADC).
He was
not talking about the power of the headphone, which it does not produce, only receives.
What he was saying was with regards to sensitivity and impedance. His headphone was a 42ohm headphone with a sensitivity of 100dB/1mW. 42ohms is not far out of where most circuits produce the most power, ie, at 32ohms, so power might not even have begun to drop off yet. The second figure means that given 1dB of input, and the right digital signal gain, it has the potential to hit 100dB with just 1mW of power. Smartphones have around 5mW at 32ohms (and probably still have as much by 42ohms), so there's the likelihood that with a Loudness War recording (ie, 99% of every album from the last ten years that isn't an audiophile release), you can blow out your eardrums with the same headphones even before you start clipping the signal.
But I'm sorry for the fact that you asked for your time since I understood practically nothing, especially when you got to talk about cars since I also do not understand about them, so I told you a while back that analogies are not your strong point. But come on, my cell phone is a Lenovo Vibe C2 and the headphone I intend to feed is a Brazilian called Kuba Disco. Knowing this information could you repeat what you just said, in a more summarized and easier way for a noob as I understand it? 
