"Great minds think alike" means that great people think about things in similar ways. Example: "I was just thinking to call you, then the phone rang and it was you calling me." Reply: "Great minds think alike." It is fun to say "Great minds think alike" because you are making a connection with the other person by saying that the two of you, in thinking the same thing at the same time, both have great minds. Example: "This summer I've decided to take scuba diving lessons." Reply: "Really? Me too. I have already paid for the course." Answer: "Great minds think alike." When you and another person think the same thing at the same time, one of you might say, "Great minds think alike."