Bioterrorism involves the use of biological weapons for the purpose of committing terrorism. The release of an infectious agent such as anthrax, smallpox, or ebola would have devastating health effects on those affected, and overwhelm the ability of local medical services to treat the infected resulting a potentially large loss of life.
Bioterrorism has historical roots. For example, it was not uncommon in medieval warfare to catapult diseased animals into a sieged city, or infect a city's water supply with diseased animals or bodies. In 1763, during the French and Indian War a British General Lord Jeffrey Amherst supplied blankets from smallpox patients to a local Indian tribe for the purpose of reducing their numbers. 
Modern biowarfare and bioterrorism
Biowarfare and bioterrorism has become even more deadly with the development of genetic engineering which allows terrorists to design germs and viruses to be resistant to antibiotics and to take on new and deadlier traits.
Prior to the signing of the ban on Biological and Chemical Weapons signed by Richard Nixon, the USAMRIID facility at Fort Detrick, Maryland was a testing and development center for biological weapons.  However, this was in response a pursuit of biological weapons by the USSR. Since 1974, USAMRIID has become one of the world's leading infectious disease research facilities.
The Soviet Union developed a number biological weapons including Smallpox and Anthrax.
Iraq is known to have had biological weapons capability prior to the Iraq War. Saddam Hussein controlled significant quantities of biological weapons which have yet to be found. Saddam may have provided some biological weapons capability to Al Qaeda.