Someone who is "aggressive" is forceful and quick to attack. "Aggressive" behavior threatens people:
Man, he's so aggressive all the time. He needs to just chill out.
You can talk about animals as being "aggressive":
You can pet her. She's not aggressive.
Being "aggressive" is usually bad, but in certain situations, the word "aggressive" can have positive associations, like in sports or in sales:
You've got to be aggressive and go for the win.