To surpass means to outdo someone or something, to go beyond what was expected. If you do better than you think you will, you will surpass your own expectations.
Some words seem to exist just to give an extra oomph to your speech, and surpass is one of these. While you could just say passed or even outdid" saying surpass seems to indicate that a person (or some other thing that performs, like a company) has really gone beyond anything you anticipated. People tend to use this word a lot before the words expectations and predictions among others, because of course surpassing is all about "surpassing something."