A homeomorphism is a concept in topology that describes a special type of mapping between two spaces. Specifically, it is a continuous function that has a continuous inverse, meaning that both the function and its reverse can be drawn without lifting a pencil from the paper. This property allows two shapes to be considered "the same" in a topological sense, even if they look different geometrically. For example, a coffee cup and a donut are homeomorphic because one can be transformed into the other through stretching or bending, without tearing or gluing. This idea helps mathematicians understand the properties of spaces that remain unchanged under continuous deformations, emphasizing the importance of shape over size or exact form.