If something is quaternary, it's either the fourth in position or exists in a group of four. If you're the fourth child in your family, you can describe yourself as the quaternary sibling.
In geology, the Quaternary Period (also known as the Age of Humans) got its name from being the fourth named period of geologic time. Although scientists now classify these periods in a new way, and it's no longer the fourth, the Quaternary kept its name. In math, a base four numerical system is also called a quaternary. You'll almost always find this adjective in a technical or scientific context. It derives from the Latin quater, "four."