Bitrate means the data rate (i.e. how many bits get transferred in a certain amount of time), usually expressed in bits per second.
The common units of bit rate are kilobits per second (Kbps) and megabits per second (Mbps). In data rates, the multipliers "k", "M", etc. stand for powers of 1000, not powers of 1024.
The term is also commonly used when discussing digital sampling and sample rates. For example, the MP3 audio compression algorithm is often set to ouput files with a bitrate of 128 kbps. This means that the file contains an average of 128 kilobits for each second of audio (960KB per minute). This contrasts with CD audio, which is encoded as 44100 16-bit stereo samples per second: 1411.2 kbps (16bit x 44100Hz x 2 channels).
Often, upper-case units and multipliers are used for bytes (like "KB" for kilobytes) and lowercase multipliers are bits (like "kb" for kilobits). All modern computers use 8-bit bytes.
MP3 bitrates can be deceptive. For example, a 128 kbps "constant bitrate" (CBR) MP3 will use about 128 kilobits for each second of audio that is encoded (so the file size, in bits, divided by the audio's duration, comes out to about 128,000), and its frame headers will occur at regular intervals, but internally, from frame to frame it may encode audio at a bitrate higher or lower than 128 kbps through the use of the bit reservoir (the ability of a frame to use spare bits from the preceding frame). However, the size of this reservoir, and thus the amount of variability, is limited, so 128 kbps will be very close to the effective bitrate across the whole file.
As another example, a "128 kbps VBR MP3" is usually a misnomer, since the point of VBR is to allow each of the MP3's internal frames to have its own bitrate. When people refer to the bitrate of a VBR MP3, they are usually referring to the actual average of bitrate of its frames. If the duration of the encoded audio is known, then "bitrate" might be the size of the file data divided by its duration, which will be pretty close to the same number. However, the duration of a VBR MP3 cannot be accurately determined without scanning all the frames.