When you grope for something, you try to get a grip on it. If you drop your flashlight in a dark cave, you might grope around for it. Beware of snakes!
If you're asked a question and you grope for an answer, you're at a loss for words. You can also grope another person, although I wouldn't recommend it: grope is usually used to describe touching that is unwanted (i.e. creepy behavior). If you do grope someone, don't bother groping for an explanation when you get slapped or arrested.
