A headphone amp is used to boost a line level signal (or just a weak signal) into something capable of properly driving headphones. It's exactly the same idea as a speaker amp, just on a smaller scale.
As long as your headphones use the connection output by the dedicated headphone port (probably 1/8" mini) then yes you should see a benefit. That benefit depends largely on the impedance of those headphones, it could range from virtually none to quite large. Typically amps are used on high impedance audiophile type headphones which need a lot more power to drive than a typical portable device or sound card can provide. In some situations there will be a substantial quality improvement with an amp but a "headphone amp" on a sound card is not likely to provide a huge increase in quality.
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