When you do something aggressively, you act in a forceful and often hostile way. Aggressively tackling someone in football is generally fine, but aggressively shoving to the front of a line is not.
The adverb aggressively means "with aggression" or "in a combative or threatening way." Think of military troops moving aggressively into enemy territory. You can also use this word in a slightly gentler way to describe something done forcefully or assertively: "They're marketing their cupcakes so aggressively — I see those ads everywhere I go!"