A biological weapon was a weapon that operates by spreading a pathogen such as a virus or a bacterium to the intended targets. This weapon is generally either lethal or at least physiologically devastating to those afflicted.
The Tarellian civilization was wiped out by biological weapons during a civil war, leaving a small number of plague-carrying survivors who escaped, typically infecting the populations of other planets after establishing contact. (TNG: "Haven")
The Dominion at times used biological weapons to make examples of populations that resisted their rule, including the Teplans, afflicted with the blight, and the inhabitants of Boranis III. (DS9: "The Quickening", "Inter Arma Enim Silent Leges")
The Brunali created a spaceborne virus that they then used to infect the Borg via children they deliberately allowed to be assimilated. Icheb was one such child, who (unknowingly) successfully transferred the virus to the Borg cube that assimilated him, killing all of the crew except for those Borg drones still in their maturation chambers. (VOY: "Collective", "Child's Play")