Here are some possible reasons why your CD doesn't play on a standard CD Audio player:
• You burned a data CD (CD-ROM) instead of an audio CD (CD-DA).
• You used a rewritable CD (only compatible with a CDRW) instead of a standard WORM (Write Once, Read Many) CD (compatible with all kinds of devices, including CD Audio players).
• Your software isn't fully RedBook compatible. The "free" software that comes with CD Burners is usually not RedBook compatible, although this doesn't guarantee that it won't work.
• You burned the CD too fast. Depending on the actual mechanism inside, and depending on the actual blank CDs you are using, and depending on the quality of the CD Audio player, it's possible to misread the data on a CD which is burned too fast (the laser doesn't get a chance to literally burn hot enough). This could be anywhere between subtle distortions and noises, to outright total garbage, to not reading it at all. Try burning at single speed, instead of 4x or 8x.
• You already had data (CD-ROM) written to this CDR, and tried to burn your audio as a SECOND session. Audio must always be the FIRST session. CD Audio players can only read the FIRST session, but computers can typically read all of them.