In a nutshell, bit rate is the speed that a bit of audio will travel. This is calculated as Kbps (kilobytes per second). As the bits are increased, the quality of the sound goes up. This is similar to a video's frames per second, where more frames equals a better picture.
The type of file that a piece of sound is converted into is related to how high the bit rate needs to be in order to get a good quality sound. AAC (ITunes), WMA (Windows Media) and RAX (Napster) are all comparable at the same bit rates with no overtly discernible difference. However, MP3s must be encoded at roughly two times that of those formats to reach the same level of sound quality.
This refers to the bit rate of files downloaded from your music service of choice. For example, Napster has a download bit rate of 192 Kbps while standard iTunes downloads are at 128 Kbps.
This measures the quality of music that you can listen to online in "real time," without downloading it. The streaming bit rate usually depends on the speed of the Internet connection.
When recording in a digital audio workstation, composers have the choice of setting the bit rate or depth at which they'll record and the sampling rate.
Bit depth in this sense refers to the number of bits actually captured during recording. The higher the bit depth, the more audio that was caught. The common bit rates are 16 (CD quality) and 24. Each has its own resolution; 16-bit has 65,536 bits and 24-bit has 16,777,216 bits. There's also 32-bit float point, but it will convert to 24-bit when mixed down.
Recording at a higher bit rate and sampling rate will increase the size of the sound file, up to 3.5 times. Make sure you have the hard disk storage space needed to hold all of that sound.