To better understand RNA, first realize that it is essential for the information in DNA to remain stable. You can think of the DNA as the "master copy" of a computer program. When you get a new program, you first copy it from the purchased disk onto the hard drive and use that copy of the program for your daily use. You store the original copy of the program away and only use it if the working copy of the program crashes. If DNA information were to be used regularly in the cell, it could accumulate errors, which would be passed on from one generation to the next. Before too long, the DNA would have so many errors that it would lose important functions and wouldn't be able to support the organism. Just as a clever computer user avoids being stuck with a corrupt program by making and storing a master copy, cells use copies of their genomic information for the working processes in the cell. These copies are made of ribonucleic acid, RNA.
Most RNAs function in an information carrying and/or processing mode in the cell. The overall information processes of the cell are given in the Central Dogma of Molecular Biology: DNA makes RNA makes Protein. RNA is involved as a carrier of information, and as a catalyst for the synthesis of the peptide bond.
That's it in a nutshell, but for much more detail about the purpose of RNA and how it functions, turn to CliffsQuickReview Biochemistry II.