Incapacitation takes a number of forms but common amongst all is that the incapacitated unit cannot move, initiate engagement or disengage, fight personally or cast. Some forms will leave the unit in a state where a single blow will croak (or dust) it. Other forms will require the unit to be healed before the next turn or they will croak. Sometimes the unit is unconscious and other times they are conscious and still able to give orders and communicate.LIAB Text 39
There are some unique forms of incapacitation that are more or less permanent, but will not necessarily croak the victim at end of turn.
A unit with leadership may no longer grant it's bonus if the incapacitation has left it unconscious.
Incapacitated units which can be croaked with a single blow are likely units who are incapicated due to significant wounds they have already sustained or who have been incapacitated in a way that leaves them more prone or susceptible (e.g. frozen so that a single blow shatters them).
Similar states in other games
Other games have analogous states. D&D has "alive, but with negative hit points." Most JRPGs has a KO status.