Homotopy is a concept in topology, a branch of mathematics that studies the properties of space that are preserved under continuous transformations. It describes a way to transform one continuous function into another through a series of intermediate functions, all of which are continuous. If two functions can be transformed into each other in this way, they are said to be homotopic. In simpler terms, homotopy allows mathematicians to classify shapes and spaces based on their ability to be stretched or deformed without tearing or gluing. This idea is crucial in understanding the fundamental properties of spaces, leading to important concepts in algebraic topology, such as homotopy groups and homotopy equivalence.