REPL: read/eval/print/loop (think irb from Ruby, although there's more to it). http://en.wikipedia.org/wiki/Read%E2%80%93eval%E2%80%93print...
Instarepl: A portmanteau of instant and REPL, meaning a REPL that evaluates immediately as you type.
"context for the Instarepl": essentially the namespace in which the REPL executes, meaning that if you run lein-light inside your project folder you can get access to your project's functions inside LightTable.
leiningen: Clojure's most popular build tool and vector for plugins that enhance the build cycle. https://github.com/technomancy/leiningen/