why do i need an amp? as far as i know it has 25 ohms
The impedance may be 25ohms, but the sensitivity is 91dB/1mW, which is a bit low. That seems high if you take it like it literally means you can go from silence at zero volume to 91dB with, like, two presses of the + button on a smartphone, much less without a lot of distortion if you even really hit 91dB at any point. For reference, the Beyerdynamic DT770 might have 10X the impedance at 250ohms, but since its sensitivity is 96dB/1mW, the HE400se will need 4X the power just to match its output. Heck the old HE400S is 22ohms, 96dB/1mW - you can far more easily drive that with a USB powered amp (and not the new ones that have a separate USB-C just for power either). Power input to dB graph is logarithmic, so every 3dB gain requires doubling the input power. By contrast an IEM like the Westone2 has a 33ohm impedance, but with a sensitivity of 117dB/1mW, any smartphone will have enough power for it.
That's just power quantity so far though. We're not yet at how much noise and distortion is in that power, hence cranking up a smartphone will not get you as far as an amp before the sound starts changing (and not for the better either). Load impedance also affects how the amp interacts with the amp, and in the most basic way, it will affect how much power the amp will spit out at a given impedance. This is why a Schiit amp for example will include ratings at 16ohm, 32ohms, 64ohms, 120ohms, 300ohms, and 600ohms; and it's not always guaranteed that it will keep going up in one direction, like how some amps will have power output lower below 32ohms or 16ohms, or how an OTL amp will produce the most power into 300ohms and then drops as the impedance rises or drops. Distortion characteristics and how it controls the driver can also change, particularly if the output impedance is high. In some cases some IEMs even require some kind of portable amp, not because it needs more power, but because it needs power that gets produced with an ultra low noise floor hence the need for a battery-powered amp that isn't trying to produce power at the cost of noise performance while also having low enough impedance that a low impedance dynamic driver IEM would still move without the amp losing control.
Think of the sensitivity like the weight of a car while impedance is a mix of unsprung weight (ie the wheels and tyres), tyre geometry and tyre compound, aerodynamics, etc. Sure lighter wheels, tyres, and brakes can make it easier for the engine to spin them and will help acceleration, and can help how the car can power out of corners, while aerodynamics can impact the top speed...and yet your acceleration and top speed are still primarily determined by the engine output. A 25ohm, 91dB/1mW headphone is sort of like having a nice handling Bentley chassis with a Camry V6 powering it, while a high sensitivity headphone or IEM is going to be like how you wreck the balance of a Lotus Seven kit car by stuffing a big block V8 into it. What you're looking for is more akin to having a Corvette or S2000 with the engines that Chevy and Honda put in there.
and what are the pad adapters for?
To fit Brainwavz HM5 pands when you wear out the stock pads because unlike Sennheiser, AKG, and HiFiMan, Philips don't sell earpads. They expect you to throw out the whole headphone once the pads are worn so they earn money selling another headphone unlike Sennheiser making money selling you $60 earpads. (That said, you don't have to give Sennheiser $60 for earpads - you use a mount adapter and mount HM5 earpads on it; I just cut up the stock earpad and fit the HM5 pads onto the plastic frames on the Sennheiser pads.)
