When a government is split into two houses, or assemblies, one of them — the "upper house" — is called a senate. The main job of most senates is to take a second look at legislation after it's been passed by the lower house.
The idea of a senate as a legislative assembly goes back to the founding of Rome, around 750 B.C.E., with the word taken from the Latin senatus, meaning "highest council." That word, then, is thought to come from senex, meaning "old man," in this case probably meant as a form of respect for wisdom. The word later grew to include national government, and the United States took the word in 1775 to refer to the upper level of the legislature. Today, you can get elected to a senate even if you're not an old man.