If you laugh with a dainty tee-hee-hee, you giggle. Children giggle a lot. Big strong men are more likely to guffaw or issue a big belly laugh.
The word giggle has been around since about the 16th century, and yet, it has no Latin or Greek roots. Most likely the word is an imitation of the silly sound you make when you laugh like this. If you and your friends have hidden a frog on your teacher's desk, when she enters the room and moves towards it, you will probably begin giggling — you know something funny is about to happen and you're a little nervous about it.