Most games handled music as instructions for the sound processor to generate specific sounds (basically, a digital score), which is today referred to as chiptune music. CD-ROM titles represented the first time developers were able to combine standard gameplay instructions with the ability to stream background music off the CD (an example of why CDs were originally referred to as a "multimedia" format).
In the 16-bit era, this was frequently used by titles released for consoles like the TurboGrafx-CD and Sega CD as well as computers like the FM Towns. By recording an actual music track, composers could use real instruments and completely bypass the limitations of the console's on-board processor. Examples are the wailing guitar soundtrack for Final Fight CD, or Tommy Tallarico's synth-rock work on the SCD version of The Terminator.
Redbook audio also rendered expensive MIDI synth modules for computers (like the Roland MT-32) and some similar sound card features unnecessary for games. Developers no longer needed to focus on making consoles that could create realistic, arranged music when they could simply play it back off a CD.
Some games also used red book tracks for cutscene audio, allowing for recorded dialogue from real actors. The TurboGrafx-CD version of Ys I & II and the Sega CD versions of Snatcher and Silpheed are examples of this. Dialogue in the game is stored as text, but every spoken cutscene's audio is stored on the CD as a red book track, and synced with the graphics on playback. Other companies would use the red book tracks for secret messages or inside jokes - such as Digital Pictures' reoccurring "Number Nine" message on Track 2 of most of their games.
Games using Redbook audio can be placed into a standard CD player, essentially letting the game CD double as a soundtrack CD. Game audio tracks appear starting at Track 2, and containing up to 30 or 40 tracks depending on the way they are organized for the game.
Track 1 on a CD with redbook audio is always the data track for the game. Customers were always strongly warned to NEVER play the data track, or risk blowing their speakers. This may happen if the stereo is turned up stupid loud, but more likely, you'll just hear a rapid scratching noise.
Redbook audio is mostly outdated for modern games, as there are better compression formats (MP3, AAC, OGG Vorbis) which can deliver equivalent or superior results at a much smaller file size. These audio files are stored with other game data, and so are not accessible through a standard CD player.