To be aware means to know about. If you're aware of a sled zooming towards you, move! And if you’re aware that the other kids wish they had sleds, share yours. That’s being socially aware. Well done.
Aware is a close relative of beware, "look out for." Julius Caesar is famously warned to "beware the ides of March." Too bad he's not aware of why. Beware and aware share the root ware, from an Old English word meaning "careful." Be aware of your purse at all times, and beware of the snatch-and-grab thief.