What They Do - these slightly contradictory physical requirements make the center position sound demanding, and it is. The center position is usually where the defense catches up with the ball movement in the backline, meaning that the centers are more likely to get tackled carrying the ball at full speed more often than any other position players.
By that same token, centers will be making more tackles on defense than other members of the backline as well, and they will generally be hitting other centers or pack players as play breaks down, meaning not only that they are involved in more tackles than other backs, but they also end up hitting people the same size as, or larger than, themselves.
This is the way an effective rugby back line is supposed to work. Ideally, on offense, the centers provide a link from the halfbacks to the wings and fullback, moving the ball quickly to the other side of the field before the opposing defense can pursue. In fact, the flyhalf will communicate the manner in which the backline will complete this maneuver right before receiving the ball from the scrumhalf.
In real life, what usually happens is that the opposition backline and flankers close on the offense by the time the ball gets to one of the centers, at which point the center with the ball will either get tackled, ending the first phase of the offense, or will exploit a gap in the defense and either kick or run with the ball, re-orienting the offense. In both cases, unless the center scores, both centers are likely to absorb punishment, either getting tackled as the ball carrier, or as the first person to form a ruck or maul on the ball carrier.