Reversing network hashpower
In theory, this attacker owns enough computing power that they could execute a "double spend" attack. They could spend coins in one place, allow the coins to enter the block chain as normal until the required confirmations are met, then fire up their 51% of the miners to craft a fraudulent fork of the block chain in which those coins were never spent, allowing them to re-spend the coins. This could theoretically be repeated for as long as the attacker maintained control of 51% or more of the hashrate.

Realistically, 51% is only the point at which this becomes possible not the point at which it becomes likely or easy. An attacker would probably need something like 65% to actually execute such an attack.

What can an attacker with 51% of hash power do?