The Game of Life is a very famous celluar automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its progression is determined by its initial state and requires no further input. You interact with this game by creating an initial configuration of cells and observing how it evolves.
A cellular automaton is a program that operates on data which represent "cells" - typically stored in a 2D grid. It consists of a collection of cells which, based on a few mathematical rules, can live, die, or multiply.
Each round of the game examines the current state of the cells, and then produces an entirely new generation of cells based on that state. Depending on the initial conditions, the cells form various patterns throughout the course of the game.