A Starfleet brat was a nickname for the child of one or more officers in Starfleet. "Starfleet brats" often grew up on starships or outposts far from home because of their parents' assignments. Valerie Archer was supposedly one such child. (VOY: "In the Flesh")
Other examples of "Starfleet brats" include Geordi La Forge, Wesley Crusher, Jake Sisko, Clara Sutter, Harry Bernard, Naomi Wildman, and Molly O'Brien.
The term is derived from the real-life term "army brat" which refers to the children of army members, who often grow up on or near bases all over the world. Jeri Ryan was an "army brat".