The aggressor's job was very easy in the original game, but became slightly more difficult with the addition of starbases in Entrenchment, although this is debatable.
Victory and defeat for your entire team usually rides on your ability to manage a balanced offense and defense on the front lines. A good economy can be useful, but the military should come first. Your top priority in this position is to maintain a powerful and competitive military. Aggressors need to play aggressively, threatening enemies and attempting to damage or cut them off at every turn. In the most common 5v5 games, most players spawn with an ally on one side and an enemy on the other: their job is to stay alive and to destroy that enemy if they can. You're the military muscle of your team, seeking out enemies and attempting to destroy them. As well, as the game changes your situation may change with it.
These roles are more like guidelines than rules, and your actual situation might be a combination of multiple positions.