To overstate is to exaggerate or place too much importance on something. Your parents may overstate the dangers of driving on icy roads to scare you into being extra careful.
If you want your brother to help you move some furniture, you might overstate how much your back hurts. And, if you're ready for lunch but your friend is dawdling, you'll be tempted to overstate how cranky you get when you're hungry. More seriously, politicians have been known to overstate the threat of terrorism or other dangers in order to gain support for a bill or a candidate.