A biohazard was something that was dangerous to organic matter.
One of the cargo containers in cargo module 4 aboard the ECS Fortunate was labeled as biohazard. (ENT: "Fortunate Son")
Enterprise NX-01 featured a bio-hazard locker for the storage of such matter in cargo bay one. (ENT: "Impulse")
Plasma coolant was considered a biohazard because it would react violently with organic matter, liquefying it on contact. (Star Trek: First Contact)
In 2376, Harry Kim commented that a dirty plate left in the Delta Flyer's replicator was a biohazard. (VOY: "Memorial")