A severance is the ending of a connection or relationship. A terrible argument between you and your cousin could turn into a all-out feud and eventually a complete severance between the two branches of your family.
The noun severance implies a separation or cut of some kind, like a severance between your father and the political party with which he has become disenchanted. If you cut off relations with a person, group, or organization, you've initiated a severance. The phrase "severance pay" means the deal a company offers to an employee who's being fired. Severance comes from the word sever, "to cut," whose origin is the Latin separare, or "separate."