PortAudio is a cross-platform Audio I/O library that is used by Audacity. PortAudio development is led by Phil Burk and Ross Bencina, but some of the Audacity developers are major contributors to PortAudio as well.
Their website can be found on: http://www.portaudio.com There are two major versions of Portaudio available, and different versions of audacity use both.
This is the "stable" version of portaudio, but has limited support for more modern audio APIs. In particular, there is no ALSA support available on Linux. Our version has been patched extensively to get the Mac CoreAudio support in particular to work with a wider range of devices.
This is the "development" version of portaudio, and has been for the last four years or more. The API is more or less stable, but the degree of completeness in the implementations is variable. There are no releases so we rely on SVN snapshots of the codebase. It is the only way to get ALSA support under Linux, and has more support on other platforms. Unfortunately progress towards a stable release seems to be slow, so often the version used in Audacity has patches that have yet to make it back into the PortAudio SVN.