CD-ROM's are pre-processed data stored on a CD that cannot be changed but can be copied in some cases.
A good example of what CD-ROM's are used for is software and games where the user can open and run the contents of the CD but cannot modify what is contained on the CD.

CD-R's are CD's that can be burned or written to once and only once. The data on a CD-R is compiled to allow a certain amount of data (roughly 700MB) to be written to the disk and the contents cannot be modified again, you can copy contents from a CD-R though.
An example of this is multimedia CD's for music or videos under 700MB.

CD-RW's are re-writable CD's that can be re-written a dozen or more times, the content can be copied, deleted and modified as necessary.
Again, an example of this multimedia and data CD's of which these format of CD's are used for most often.