Nullity pertains to an act or proceeding which has no force or effect under the law. For example, if a court judgment declares the nullity of a marriage, this means that said marriage has no legal effect, and can be treated as if it never happened at all.
The nullity of an act or proceeding means that it has no effect, and therefore does not exist in the eyes of the law. Hence, a party to a marriage which was declared a nullity by a court can be safely assured that his/her succeeding marriage will be considered legal.