BoomForge is a shared plugin framework for a family of related WoW addons. It has no user-facing features on its own, installing it alone does nothing. If you were told to install BoomForge, it's because another addon lists it as a required dependency.
What it does
BoomForge hosts one shared copy of the Ace3 library family (AceAddon, AceConsole, AceEvent, AceTimer, AceHook, AceDB, AceLocale, AceGUI, AceConfig) plus LibDataBroker, LibDBIcon, and LibSharedMedia, so that dependent addons don't each need to bundle their own copies. It also exposes a small plugin-registration API and a shared debug/logging helper that dependent addons use internally.
For end users
Just install it alongside whatever addon required it. There's nothing to configure.
For addon authors
Add ## RequiredDeps: BoomForge to your .toc and call BoomForge:RegisterPlugin(self, { name = "YourAddonName", version = "..." }) on load. See the project README on GitHub for details.