All this data is potentially out of date, and should be taken with a truckload of salt
Hot Dropping is a tactic whereby a cynosural field is opened, usually by a frigate or other small maneuverable ship on grid with a hostile target, allowing attackers to jump directly into a battle from a different system. This tactic allows additional firepower to be quickly brought to the battlefield, with the target ship(s) often having no more than a few seconds warning before the arrival of hostile forces. It works with both capital ships (equipped with their own (jump drives), and non capitals (which can be jumped by a titan's jump bridge). Covert Ops capable vessels can also be bridged by a Black Ops battleship.
Hot dropping is used in several different ways. The tactic was commonly used to drop carriers or Motherships onto ships in lowsec systems before the advent of heavy interdictors. At the time, motherships could only be prevented from jumping by interdictor bubbles, which can only be deployed in 0.0 space. This made motherships practically invincible in lowsec.
Hot dropping is often used in ambushes against unsuspecting hostile ships. The tactic is also used in conjunction with some kind of bait, typically a small number of capital ships or a seemingly undefended control tower, intended to entice a hostile force to commit to battle. When the hostile forces have committed, a superior force of ships are then hot dropped on top of them.
A hot drop also allows the ambushers to position their fleet in an optimal position to gain an advantage over their target. A textbook example of this can be seen in the 0-W778 Capital Ship fight of 20-12-2008, where a Goonswarm capital fleet waited for Band of Brothers to deploy their close-range capital ships, then countering by deploying a cyno at long range and hotdropping with sniper fitted dreadnoughts. Massed interdictor bubbles and other tackling support ships were deployed on the BoB capitals to prevent them from escaping or warping to closer range, resulting in BoB's loss of 49 capital ships to Goonswarm's 10.
The origin of the term may be the result of a kill on a Goonswarm carrier made by The Establishment, a pirate corporation well reputed at the time for pioneering the tactic with their infamous Mothership.