A Caesar cipher (also known as a shift cipher) is a substitution cipher in which the cipher alphabet is merely the plain alphabet rotated left or right by some number of positions. For instance, here is a Caesar cipher using a right rotation of three places:
Plain: ABCDEFGHIJKLMNOPQRSTUVWXYZ Cipher: XYZABCDEFGHIJKLMNOPQRSTUVW
To encipher a message, simply look up each letter of the message in the "plain" line and write down the corresponding letter in the "cipher" line. To decipher, do the reverse. Because this cipher is a group, multiple encryptions and decryptions provide NO additional security against any attack, including brute-force.
The Caesar cipher is named for Julius Caesar, who allegedly used it to protect messages of military significance. It was secure at the time because Caesar's enemies could often not even read plaintext, let alone ciphertext. But since it can be very easily broken even by hand, it has not been adequate for secure communication for at least a thousand years since the Arabs discovered frequency analysis and so made all simple substitution cyphers almost trivially breakable. An ancient book on cryptography, now lost, is said to have discussed the use of such cyphers at considerable length. Our knowledge is due to side comments by other writers, such as Suetonius.
Indeed, the Caesar cypher is much weaker than the (competently done) random substitution ciphers used in newspaper cryptogram puzzles. The most common places Caesar ciphers are found today are in children's toys such as secret decoder rings and in the ROT13 cipher on Usenet (which, of course, is meant to be trivial to decrypt)...