Simplifying the language, the audio interface is what allows you to pass the sound to digital signal, which is what your computer can read and process.
With the advancement of technology, there is a growing trend of abandoning analogue equipment to become digital. Therefore, everything that we want to record must be able to be processed by the computer and by the production software.
Well, the audio interface is the equipment that captures those analog signals that your synthesizer or any instrument emits and converts them into digital signals, giving audio quality and making them capable of being treated by the computer. For that reason, an interface is something that we can not do without in our study. If we want to make music at home, we need a sound interface.