If you grope for something that you cannot see, you try to find it by moving your hands around in order to feel it.

If you grope your way to a place, you move there, holding your hands in front of you and feeling the way because you cannot see anything.

If you grope for something, for example the solution to a problem, you try to think of it, when you have no real idea what it could be.

If one person gropes another, they touch or take hold of them in a rough, sexual way.