I have average IQ so even after reading several articles on Paxos, I was still confused.
Then I found this presentation from Google - it is just 20-ish minutes but provides a super clear explanation to what problem Paxos solves (that's where I got lost!), how it works step by step and ends with a simple distributed data storage system as an example. So, I'd highly suggest watching this video first:
https://www.youtube.com/watch?v=d7nAGI_NZPk
Then, you'll find Paxos Wiki is more approachable: https://en.wikipedia.org/wiki/Paxos_(computer_science)
And, here is a very good real-life application to Paxos algorithm(in zh-cn): https://www.jianshu.com/p/dbb7da189b51