Germ warfare is, these days, more typically known as biological warfare. It is the use of biological agents to kill or incapacitate your enemy in war or to destroy the enemy's resources.
For example, during World War II, the Japanese experimented with trying to spread bubonic plague by dropping infected fleas from airplanes. This did not really come to anything, but it would have been germ warfare -- trying to kill enemies by making them ill.
Another example would be if someone introduced a really bad disease of (for example) corn to the American Midwest. If an enemy did this, they might (if they were successful) really hurt the American economy.
Germ warfare is when pathogens, such as bacteria and viruses or any toxin that can cause disease, are used as a weapon. The intention of using this kind of warfare is to cause mass devastation and generally kill masses of people. Some examples of living organisms that could be used in germ warfare are anthrax and yellow fever virus. Toxins would refer to certain poisons that are produced via microorganisms.
The Biological Weapons Convention prohibits the development, production, and storage of biological weapons. This does not necessarily mean that all countries are compliant with this order or that terrorist organizations would not use them.