SHA is a family of "Secure Hash Algorithms" that have been developed by the National Security Agency. There is currently a competition among dozens of options for who will become SHA-3, the new hash algorithm for 2012+.
You use SHA functions to take a large document and compute a "digest" (also called "hash") of the input. It's important to realize that this is a one-way process. You can't take a digest and recover the original document.
AES, the Advanced Encryption Standard is a symmetric block algorithm. This means that it takes 16 byte blocks and encrypts them. It is "symmetric" because the key allows for both encryption and decryption.
UPDATE: Keccak was named the SHA-3 winner on October 2, 2012.
