Almost all soundcards that I can think of are both DAC units with an amp section.
If you have a sound card and are pleased with how it sounds then there may not be a reason to upgrade.
An amp is not solely to increase the volume, but that is its primary function. Many amps and devices with amps stages like iPods are not designed with studio headphones in mind. These devices might not be able to supply enough current or voltage to the headphone, they may have too high of output impedance which can lead to poor control of the headphone driver ( look up audio damping factor ), and lastly amps with better designs tend to be quieter.
There are many thoughts regarding amps, but most studio professionals prefer their gear to be as revealing, neutral, and pure sounding as possible as to not hide what is actually in the recording. Many amps can color the sound much like headphones differ from each other. A good amp, in my opinion, should basically be "a wire with gain" and not add or subtract anything from the music.
These things are hard to tell unless they are measured because we all supply a subjective bias to the sound. We all have different ears, hearing experiences, preference, and ways of enjoying sound. This is why many of us relay partially on the measurements often conducted by outside sources to prove how the amp performs. The same can be said of a DAC and soundcard, but there are not many people out there that measure equipment.
You can dig around here:
for some examples.
It is also a way of keeping audio manufacturers honest. If there is not measured difference from amp 1 compared to amp 2, and everything else is the same excluding price, then it is often in the best interests of the buyer to purchase the less expensive amp.
I hope that helps you understand a bit more.