There's a few things...
* The analog to digital converter affects anything being recorded from "the outside" - mics, instruments, outboard effects and such...the exception being digital gear with digital outputs, which of course needn't to be converted to digital. The differences are subtle, but tend to stack up - like when you're recording a lot of out real instruments: as an example, if the converter introduces an inaudible EQ hump @ 400Hz, it'd probably become somewhat prominent if you stack ten tracks with the same hump on top of each other.
* The digital to analog converters affect the outgoing sound from the computer...but only what you hear. It doesn't change the files in any way, so it's an indirect influence. There's a lot of talk about the converters these days, but let's just say that 95% of us amateur music-makers need not to worry about them - the converters (both ways) are pretty good even in all but the cheapest of the cheap interfaces (and even the cheapest stuff is rarely so bad you'd instantly hear "that horrible conversion").
* Latency tends to affect playing, especially if you're monitoring through your DAW (instead of direct through the interface) - but that depends on what you're doing. With a guitar, even a few milliseconds can throw you off, but probably doesn't have much impact on playing, say, a sweeping, slow-attack synth pad.
* And naturally, mic preamps (which most interfaces these days have) impart some kind of qualities to the sound. These'll probably have more impact on the sound than the converters.
But all in all, the actual differences in sound are subtle, in most situations. When you have an awesome monitoring environment (ie. great room & great acoustics & great monitors), then these things start to make a
real difference. Before you've reached that point, pay attention, but don't stress it too much
Your skills the sound sources are much more bigger factors in how your stuff sounds than any of these things.