Why do girls, in general, smile at guys?

Well today at lunch I was giving quick glances at a girl. Subtly I noticed that she started to notice that I was looking at her and she was smiling a bit also. Then as I was eating lunch a small piece of food fell out my mouth (awkwardness arises) then couple minutes later I looked back at her and gave more glances, she didn't catch me this time, ha! Then I looked again and our eyes met, her eyes were beautiful! She was smiling a big smile but with lips closed.. So what does it mean? I hope she possibly was not laughing because she saw the food incident. :-/