Mining creates the equivalent of a competitive lottery that makes it very difficult for anyone to consecutively add new blocks of transactions into the block chain. This protects the neutrality of the network by preventing any individual from gaining the power to block certain transactions. This also prevents any individual from replacing parts of the block chain to roll back their own spends, which could be used to defraud other users. Mining makes it exponentially more difficult to reverse a past transaction by requiring the rewriting of all blocks following this transaction.
