There are two different flavors of WPA for home use: WPA-TKIP, and WPA-AES.
WEP and WPA-TKIP both use the RC4 encryption algorithm...the same algorithm used in SSL. The primary difference between the two is that WPA increases the IV from 24 bits to 48 bits. This solves the weak key problem in WEP and makes the key orders of magnitude harder to crack. TKIP also introduces dynamic rekeying, solving the static key problem with WEP. In WEP, the key never changed unless you walked to each device and changed it. In TKIP, subkeys are deduced from the key you input, and these change at certain intervals. This makes it even harder to crack the key.
WPA-AES uses a completely different form of encryption, AES. AES is becoming the successor to 3DES, and is already the standard method of encryption for the US Government. The NSA says it's a secure enough cipher. AES has dynamic rekeying natively built into it. AES is also hardware optimized. If your hardware can do AES, then you'll likely see better performance over WPA-TKIP. AES is eventually going to become the WPA standard. TKIP was just intended as a stop-gap until hardware vendors can place the processors needed to do AES into their products. Not every access-point can do AES because some lack the processing power to handle the mathematical operations.
Hope this helps you understand the difference.