CD-R is short for "CD-Recordable". Recordable CDs are WORM (Write Once, Read Multiple) media that work just like standard CDs. The advantage of CD-R over other types of optical media is that you can use the discs with a standard CD player. The disadvantage is that you can't reuse a disc.
A related technology called CD-Rewritable (CD-RW) allows you to erase discs and reuse them, but the CD-RW media doesn't work in all players. CD-Rewritable drives are able to write both CD-R and CD-RW discs.
All CD recorders can read CDs and CD-ROMs, just like a standard CD-ROM drive.
Everything you ever wanted to know about CD-R and CD-RW discs, including technical information, common problems and solutions, and what to do with discs that failed to burn correctly.