Well technically you can google or wiki all these up. The ones that I pay attention to most are the one I know will have some direct effect in the sound quality/energy demand:
THD (total harmonic distortion)
Input Impedance (resistance/ohms)
Sensitivity (SPL, for headphones usual db @ 1khz)
SNR (signal to noise ratio)
What I don't pay much attention to are frequency range (although important for recording purpose), and made up specs/mystical properties that are famous by Bose and the all time king of bs, Monster Cables. Also exaggerated chemical properties that are the norm in standard but written in long syllables as if they are special.
For SNR, there is a lot of debate on the dynamic range of CD quality, but it's going to be somewhere are 90-96.32db, but that is theoretically minus other factors.. So I aim for mp3 devices that can do atleast 90db SNR or higher. Ofcourse we're crossing into the sound science territory and I'm not trying to bring up some debate. Especially for the people who are listening to tube and vynil.
SPL and impedance can effect how well your source or amp drive the headphone or speakers. If your mp3 output 32mW per channel @ 16ohms and it's driving a headphone with 300ohms and 80db SPL, you'll barely get any sound out of it, but if you drive an earbud with 16ohms impedance and 108db spl, then you can get the volume to ear damaging level.
Something might have good spec but doesn't sound the way you like because each devices can have different sound signature, for example the E-mu 0404 (pci), good spec but extremely aggressive to my liking, the most reliable way is to read alot of reviews from other people. I have come to kind of associate a particular sound signature to a particular brand, it's not always correct ofcourse. Whenever I think Sony, I think ear bleeding.
