Something homologous is similar in function to something else. You might say that your dog's hind legs and your legs are homologous, because they have similar structure and function.
Homologous comes from the Latin for "agreeing," and has the root homo- in it, which means "same." In biology, homologous either refers to traits that share an origin, and have the same function (like the spine on all vertebrates), or structures that share an evolutionary origin, but have developed different functions. Either way, something is the same about them. You'll also find homologous in math, like when two triangles share a line.