Chromaprint is the core component of the AcoustID project.
It’s a client-side library that implements a custom algorithm for extracting fingerprints from any audio source.
The library exposes a simple C API. The documentation for the C API can be found in chromaprint.h.
Note that the library only calculates audio fingerprints from the provided raw uncompressed audio data. It does not deal with audio file formats in any way. Your application needs to find a way to decode audio files (MP3, MP4, FLAC, etc.) and feed the uncompressed data to Chromaprint.
You can use pyacoustid to interact with the library from Python. It provides a direct wrapper around the library, but also higher-level functions for generating fingerprints from audio files.
You can also use the fpcalc utility programatically. It can produce JSON output, which should be easy to parse in any language. This is the recommended way to use Chromaprint if all you need is generate fingerprints for AcoustID.