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. And if you can't find your cellphone, you might grope around in your backpack, hoping it just got buried beneath your homework. You can also grope another person, although I wouldn't recommend it: grope is usually used to describe touching that is unwanted.