A lambda expression is a way of defining a function without associating it with a function name.

The actual term "lambda" was borrowed from Alonzo Church's lambda calculus, which was a formalism for describing functions and their evaluation that predated programming.

I've used them in Lisp, Scheme, Dylan, and ML, and they are very, VERY useful indeed.

Common Lisp and Dylan try to incorporate both OO and functional programming, but in Scheme and ML the function as a data type is considered more important than the object. (Gasp. Heresy!).  As an aside, a very interesting aside is that in a dynamically typed version of the lambda calculus, you only need about 3 constructs to get complete Turing computability. Surprisingly, you can define recursive procedures without using function names or variables of any sort.

Anyhow, here's a pseudo Java example, passing an anonymous method that gets assigned to a button's action() field. I'm using "Method" here instead of "Lambda".

Button quitButton = new Button("Quit);

quitButton.action = new Method((Event e, Object o) { System.exit(0); });

functional- principal