Consensus is such an important problem and Paxos is such an important algorithm that I have to talk about them. If you ever see a web site or blog talking about distributed fundamentals and systems but not mentioning Consensus and Paxos you had better skip that web site or blog.
Why is it important? First it is so important in real world. We live under so many laws which were passed by consensus. We have so many meetings and emails at work mainly to reach agreement on something. In computer world processes/machines need to agree on many things such as committing or aborting a transaction, choosing a leader, granting a lock, replicated state machine, atomic broadcast and so on. These things are often the foundation of distributed systems and critical to higher level applications and services.
For details please read http://paullou.com/2014/05/20/consensus-and-paxos/