To grasp is to get a hold of something, literally or figuratively. Grasp the grammar textbook with both hands and then read it to grasp the rules of the English language.
It makes sense that the word grasp means understanding a concept since you are "getting a hold of an idea" just as you would grasp something tangible to hold. Grasp is good for when you're talking about comprehending the scale of something, or the full picture of a multi-faceted problem or idea. You might know that there is going to be a heat wave, but you may not grasp the idea of its relationship to global warming.