The Hebrew word here is כרת (karet). The precise meaning is uncertain, but it seems to be a punishment at the hands of heaven, not one that a human court hands down. Depending on whom you ask, this might be an early death (at the age of 50, according to one talmudic opinion), extinction of the soul (spiritual, not physical, punishment), or a punishment in the world to come (after death). The first mishna in tractate Keritot enumerates 36 transgressions for which this is the punishment, drawn from various places in torah; Wikipedia lists some of them.
Jewish Virtual Library (first link above) notes some of the difficulties in understanding this:
Every attempt toward a general rationale of this punishment involves serious halakhic and philosophical difficulties, and the problem greatly exercised the early authorities; although the halakhah itself makes a distinction between karet and "death by the hand of heaven" (MK 28a), the difference between them is not clear. Some rishonim hold that "natural" death takes place at the age of 60 (or later), when the karet period has ended, and that "death by the hand of heaven" has no fixed time, save that one's span of life is curtailed. Others hold, in accordance with the Jerusalem Talmud (Bik. 2:1), that karet comes at the age of 50, "death by the hand of heaven" at 60, and natural death between 60 and 70. The connection between the punishment of "ariri" and karet and the real nature of the former is also not clear. In the Bible the punishments of karet and ariri are frequently found together. Some rishonim hold that the minor children of a sinner are also punished through the father's karet, and in their view this also constitutes the difference between karet and "death by the hand of heaven" (Rashi, Ket. 30b, et al.). Others, however, differ (Tos. to Shab. 25a). With regard to karet in the case of the old, it is laid down that the punishment lies in the manner of death, since "one dying in either one, two, or three days has suffered karet."