I am trying to understand the difference between paxos and two phase commit as means to reach consensus among multiple machines. Two phase commit and three phase commit is very easy to understand. It also seems that 3PC solves the failure problem that would block in 2PC. So I don't really understand what Paxos is solving. Can anyone illuminate me about what problem does Paxos exactly solve?
2PC blocks if the transaction manager fails, requiring human intervention to restart. 3PC algorithms (there are several such algorithms) try to fix 2PC by electing a new transaction manager when the original manager fails.
Paxos does not block as long as a majority of processes (managers) are correct. Paxos actually solves the more general problem of consensus, hence, it can be used to implement transaction commit as well. In comparison to 2PC it requires more messages, but it is resilient to manager failures. In comparison to most 3PC algorithms, Paxos renders a simpler, more efficient algorithm (minimal message delay), and has been proved to be correct.
Gray and Lamport compare 2PC and Paxos in an excellent paper titled "Consensus on Transaction Commit".
(In the answer of peter, I think he is mixing 2PC with 2PL (two-phase locking).)