If you really need to keep it simple, then a closure is a function with its context. The function in the closure can still access the same variables it could when it was defined, no matter where you call it from. (In Lua, these are called upvalues, which I think is a very descriptive term.)
I met the concept first in Lua, and this definition helped me understand the concept. Maybe have a look at Lua: its simpleness and power is fascinating, and certainly helps to develop a certain view at other languages. Its concept of closures would be a good example to that.
