Aggression refers to a playing style where a particular player is often betting and raising instead of calling and checking and opts to play most of his hand this way.
It can be used to describe a separate action or a style of playing. For example, it can be said that the player is making an aggressive action when he 3-bets his opponent, but it can also be said that the player is very aggressive in general if he often 3-bets other players and usually plays fast.
To simplify this definition, you can imagine being aggressive simply means putting pressure on your opponents by forcing them to either fold or risk more money. Aggression is one of a poker player's most important skills because it lets you get more out of your good hands or win pots even when you don't have the best hand.
Of course, it is important to select good spots to play aggressively instead of atomically doing it every time, but it will surely help you play more sound strategy than being passive in your games.