Borg are a race of cyborgs originating from the Delta Quardrant of the Trek Galaxy, originally created by the Precursors, who are at a continuous war with the Federation, the organization that Jean-Luc Picard works for. They want to assimilate everyone in the Galaxy to become like them. Remind youof anyone?
They are ruled by a Queen who is killed by Data, after she tries to flirt with him. The stupid thing about Borg is, they won't attack you unless they perceive you as a threat. This means you can walk into their base and they won't assimilate you for some reason. They only attack civilisations, not individuals, so they'll ignore you. This means you could disgiuse a bomb as a teacosy and take it in, arm it and waltz out.
However, they are not to be underestimated. A single Borg can destroy a species. Their method of assimilation is quick and efficient, a single touch can transform you into a half-Borg, ready for complete assimilation at a Borg headquarters. They also possess projectile weaponry and dangerous blades for close quarters combat. Borg also have the ability to adapt to protect themselves from any weapon after enough are killed by it.
Borg went to war with the Mondasian Cybermen, which explains why the Mondasians haven't been seen very much since the arrival of the Parallel Cybermen. The Borg were utterly annihilated during this war because the Cyberman Remnant and the Mondasians joined forces and provided the Galaxy with a cure for Borg Assimilation.