A Homeomorphism is a continuous function between two topological spaces that has a continuous inverse function. In other words, if there exists a homeomorphism between two spaces, they are considered topologically equivalent, meaning they have the same topological properties.
The most obvious and famous example of a homeomorphism is the one between a coffee cup and a donut (torus). Both objects can be continuously deformed into each other without cutting or gluing, demonstrating that they are topologically equivalent.