A necessary condition of a statement must be satisfied for the statement to be true. Formally, a statement P is a necessary condition of a statement Q if Q implies P. For example, the ability to breathe is necessary to a human's survival. Likewise, for the whole numbers greater than two, being odd is necessary to being prime, since two is the only whole number that is both even and prime.
A sufficient condition is one that, if satisfied, assures the statement's truth. Formally, a statement P is a sufficient condition of a statement Q if P implies Q. Thus, jumping is sufficient to leave the ground, since an intrinsic element of the concept jumping is leaving the ground. A number's being divisible by 4 is sufficient (but not necessary) for its being even.
The whole concept of necessary and sufficient conditions has always fascinated me.
As in the example above. Breathing is a necessary condition for you to carry on living but it's not a sufficient condition. Pretty hard to get your head round