If you grasp something, you take it in your hand and hold it very firmly.

A grasp is a very firm hold or grip.

If you say that something is in someone's grasp, you disapprove of the fact that they possess or control it. If something slips from your grasp, you lose it or lose control of it.

If you grasp something that is complicated or difficult to understand, you understand it.

A grasp of something is an understanding of it.

If you say that something is within someone's grasp, you mean that it is very likely that they will achieve it.