An audio interface is a piece of hardware that serves as a bridge between your microphone, guitar, keyboard, or other sound-generating equipment and your computer. It provides high-quality conversion of the analog audio signal from your microphone or instrument into a digital signal that your computer can understand, and then back again for recording or playback. This process is important because the onboard sound card in your computer is not designed to handle the complexities of professional audio equipment, and using an audio interface can greatly improve the sound quality of your recordings.
Another important reason to use an audio interface is that it provides you with multiple mic/line inputs, allowing you to record multiple sources at once. This is something that most onboard sound cards cannot do.
Additionally, audio interfaces often come with additional features such as phantom power for condenser microphones, direct monitoring, MIDI inputs/ outputs, and various other I/O options.