My understanding is that the goal is double-spending. The attacker will make a transaction to a victim. The victim would be convinced it owns the coins, as the transaction appears in the chain. The attacker will then start mining a new chain (starting at a block before the transaction) which does not contain the transaction to the victim. If the attacker has enough computing power, it will be able to make the new chain the "official" one, invalidating the first chain.
