The AD/DA converter is the heart of your digital recording system. On the front end, you have the A/D converter, which will turn the analog signal from your microphone and preamp, into a digital waveform that can be played back and manipulated through your DAW. Having a quality A/D converter is key to maintaining the depth of the the original source, where a lower quality A/D can leave your digital signal sounding thin or hollow, which is almost impossible to fix through digital or analog dynamic processing or EQ.
On the back end is the D/A converter, which is what converts the digital audio from your DAW back into an analog signal that we hear back through our studio monitors. If you are using an analog desk, it is very important to have the highest quality D/A conversion. If you are using a lower quality D/A converter, you will be sending a degraded signal to your console, which will be amplified by the analog circuitry of the desk.
Some interfaces have built in preamps, as well as A/D D/A conversion. These are a great option for a smaller studio, the price point is usually a bit lower, you won’t need to buy any external analog preamps, and the conversion still maintains a higher quality. For a more commercial recording facility, you may want to look into something that just does A/D D/A conversion, as these units aren't also trying to focus on the quality of the internal preamp, more attention is put onto the converters, resulting in much clearer, full bodied audio.