Centers are the "commanders" of the offensive attack. Wingers and centers have very similar roles in the offensive zone. All 3 forwards should be working towards the common goal of causing confusion and trouble for the opposing defenders and goaltender. This is accomplished by moving constantly in and out of the slot and crease area, cycling the puck in the corners and behind the net, frequently changing the point of attack which will keep the goalie and opposing defenders guessing. This will give you and your line mates time and space to execute your offensive attack.
The center-man's most important role is to be continually assessing the play and communicating with his line mates to make sure that they are always prepared to react. As a center-man, you must be willing to be the first one into the trenches and the first one back into the defensive zone. The center not only has the "freedom" to roam around each part of the ice surface, it's his responsibility to support his line mates in every situation; whether it's in the corner digging for loose pucks, in front of the net battling for position or pressuring the defensemen on the forecheck. The center should be the hardest/smartest working player on the ice.
As a center-man, you must be able to pass the puck well, and in order to do that you must have exceptional vision on the ice. The physical act of passing the puck can be learned fairly easily, but great vision is a trait that some players are more blessed with than others. Vision, too, can be learned and developed over time. What it basically comes down to is the ability to quickly and accurately read the play and then react by making the best play possible.