A tactical nuclear weapon is a fission or fusion device, typically in the kiloton range, meant for use on the conventional battlefield. Contrast this to strategic nuclear weapons such as most ICBMs. A tactical nuke would be used, for example, to take out an armored division, or a military fortification. A strategic weapon, on the other hand, would be used to destroy or render uninhabitable larger areas, and are consequently meant to be used more as a political tool (i.e. deterrence).
Note that the 1987 Intermediate-Range Nuclear Forces (INF) Treaty between the US and USSR outlawed all short and medium range nuclear weapons, and thus all such existing weapons should have been destroyed at that time.
Tacnukes were conceived and designed back in the days when the effects of radiation were not well-understood, and most military planners viewed fissionable material as just another explosive (albeit a very, very powerful explosive). Thus, this led to proposals for weapon systems that were as dangerous to the user as they were to the target, such as the shoulder-launched nuke whose blast radius was slightly larger than its range. (Fire, duck and cover!)
Several tactical weapons have been proposed, designed, and at the height of the Cold War, actually put on the front lines. Some of them follow (feel free to /msg me with more examples):
- Short- and medium-range nuclear missiles such as the Pershing and the SS-20 are often classified as tactical weapons, although they have enough range to be used as strategic nuclear weapons.
- The Genie air-to-air missile was a Canadian tactical weapon designed to take out incoming Russian bombers flying in close formation. A few hundred were produced and deployed, although I believe none were actually used.
- The W79 Mod 0 and W82 Mod 0 warheads for the 8-inch and 155 mm artillery shells, respectively, were neutron warheads with variable yields ranging from 100 tons to 1.1 kilotons. The neutron warheads were designed specifically to defeat heavy armor by killing tank crews with an intense burst of radiation (8000 rads).
- The aforementioned shoulder-launched weapon, with a warhead in the 10-20 ton range, was the lowest yield warhead ever deployed by the US. The W54 warhead ("Davy Crockett ") for the M-28 recoiless rifle (1.5-mile range) could be carried by a two-man team, or mounted on a jeep. (A picture of the Davy Crockett can be seen at http://www.fas.org/nuke/hew/Usa/Weapons/W54davy2s.jpg). Rumor has it that W54-equipped jeeps were patrolling the Berlin Wall for a time.
In the realm of fiction, numerous authors (especially in classic science fiction) described the use of tacnukes. One of the more famous ones is Heinlein's Starship Troopers (the book, not the movie) where the MI's power armor mounted two mortars in a V on the back, each firing nuclear-tipped shells to both sides of the trooper.
One concept often thrown around in the newsgroups is the americium bullet - a certain isotope of americium has a critical mass in the milligram range, and thus an americium-based warhead could conceivably be built in the form of a large-caliber bullet (the ultimate derringer!).
Details verified from the High Energy Weapons Archive (http://www.fas.org/nuke/hew/) and the Nuclear Weapons FAQ (http://www.fas.org/nuke/hew/Nwfaq/Nfaq0.html). Thank you, Google!