What are "tactical" nuclear weapons?

Answer

Technically, a tactical nuclear weapon is any weapon that’s not been classified as “strategic” under US- Russian arms control agreements (SALTSORTSTART). Deployed tactical weapons in Europe can have explosive yields up to 300 kilotons, or 20 times that of the bomb that destroyed Hiroshima. Sometimes these weapons are also referred to as  ‘sub-strategic’ or ‘non-strategic’.  

Most frequently, ‘tactical’ nuclear weapons imply the weapons that were designed to be used on the battlefields of Europe during the Cold War. In the last century, they were deployed across the continent in case a 'hot' conflict between NATO and the Warsaw Pact were to escalate. At the end of the 1980s there were around 7,500 of these weapons deployed throughout Europe, but the mutual unilateral reductions that took place in the early 1990s brought the numbers down significantly. The Federation of American Scientists currently estimates Russian non-strategic nuclear warheads at 1,912, and approximately 100 U.S. non-strategic warheads deployed in five European countries. 

For more on the impacts of any nuclear weapon, see here.