ClojureScript is a version of Clojure that compiles to javascript code and runs in the browser.
While it is mostly the same as Clojure, there are a few differences (mainly, it lacks some api calls that invoke java functions that are not available in javascript)
Figwheel automatically rebuilds your clojurescript code when source files change and reloads code in browser. Reload works without refreshing page and you can preserve some of app's state between reloads by using defonce.
It is alternative to REPL-based development (although it includes REPL too). Instead of re-evaling changed functions in REPL, it reloads all code, and you can use println to see result of expression evaluation in browser's js console.
More details on parameters for lein-clsjbuild can be found in their example project.
All Closure event names can be found in their documentation on the EventType enum.