"lambda" term usage in programming
There is a popular formal system called Lambda calculus. It is Turing complete and has great importance in the theory of programming languages. Lambda calculus is based on anonymous functions with very simple syntax. You start a new function with a $\lambda$, list the arguments, place a dot, and write down the return value. For example, $\lambda x.x$ is the identity function, $\lambda x.xx$ applies the functional argument $x$ to itself. 

Since programming language designers know Lambda calculus very well, it seemed like a good idea to call anonymous functions in their language lambdas.