SMS or Short Message Service is part of the GSM digital cellular standard.

SMS is a "store and forward" message system which means that the message is sent from the originator to a so called SMS center, and then on to the recipient. Once the message is received in the other end, an optional confirmation message is sent back to the originator which in effect guarantees delivery. Because SMS messages are sent in the channel control, messages can be sent and delivered even if the phone's voice/data channel is occupied. SMS messages can be up to 160 characters in length, and although not all devices support it, it is possible to link 160 character messages together to form a longer message.

Mobilesms's intro to SMS
Tutorials and FAQs
An Introduction to the Short Message Service at MobileIPWorld
SMS FAQ