In the strict sense, an AD converter, or more properly and Analog_to_Digital converter is just that something that converts an analog signal into a digital representation. Generally, these AD converters contain hardware and software that have some way to transform the analog signal into an electrical inpulse and then digitize the electrical impulse.
In the music world, this translates into converting music (or some would say noise) into ones and zeros.
The current crop of AD converters utilized in music can sample at rates up to 192 kilohertz. Many people in the business consider this an overkill and pure marketing hype, due to the Nyquist-Shannon sampling theorem. Simply put, they say the analog waveform does not have enough information in it to necessitate such high sampling rates.
AD converters for musical purposes come in a variety of price ranges - from under $100 to over $10,000 for 2 channels or inputs.
There is also an opposite device - the DA converter which does the exact opposite.