A severance clause (or severability clause) acknowledges that the law may interfere with the terms of a contract, and tries to mitigate the damage to one or both parties' interests that may be caused by such interference.
Typically, such clauses begin with a statement that the invalidity of one part of the agreement will not lead to the invalidity of the whole agreement:
If a Clause of this Agreement is determined by any court or other competent authority to be unlawful and/or unenforceable, the other Clauses of this Agreement will continue in effect.
Of course, the courts will usually have something to say about this question, and in some circumstances will ignore this kind of stipulation.
More elaborate severability clauses may try to rescue the remaining parts of a contract clause after the removal of the offending words. For instance:
If any unlawful and/or unenforceable Clause would be lawful or enforceable if part of it were deleted, that part will be deemed to be deleted, and the rest of the Clause will continue in effect (unless that would contradict the clear intention of the parties, in which case the entirety of the relevant Clause will be deemed to be deleted).