Read more about its history and how it works in Circuit Simulation - Part One - SPICE Turns Thirty-Six. It's a nice article where you will either learn a little circuit theory, or have flashbacks of courses you took a long time ago. I used to be able to do these equations in my sleep. Let's not talk about my "current" capability.
If you'd like to learn more about SPICE, look for the blogger to post more parts in his series. There's also The SPICE Book, authored by one of the SPICE developers.