Bitrate describes how much data is used each second to encode audio, usually measured in thousands of bits per second (kbps).
For example, high quality MP3 files encode music at 320 kbps (320,000 bits per second).
Higher bitrates generally preserve more detail in Lossy Audio formats.
Bitrate comes in two shapes. Constant bitrate (CBR) spends the same amount of data on every second of the track. Variable bitrate (VBR) spends more on complex passages and less on simple ones, which can reach comparable quality in a smaller file. VBR is fine in most modern setups, but it has historically caused waveform and beat grid drift on some older players and software, so if you play from USB on club gear, CBR 320 is the safer choice.
The number only means something for lossy formats. For uncompressed audio the bitrate is simply arithmetic from the sample rate, bit depth and channel count, so a CD-quality WAV always works out at about 1,411 kbps. It is also worth remembering that the number describes the container, not the history of what is inside it. A file can be 320 kbps and still sound poor if it was encoded from a low quality source.
See Also
MP3, Lossy Audio, file format, and Sample Rate