Lambda calculus is a formal system in mathematical logic and computer science used to express computation through function abstraction and application. It uses variable binding and substitution to define functions and their evaluations, allowing for the manipulation of functions as first-class citizens. Developed by Alonzo Church in the 1930s, lambda calculus serves as a foundation for functional programming languages and helps in understanding the principles of computation. It provides a simple yet powerful framework for defining and applying functions, making it essential for theoretical computer science and programming language design.