This circle is used so that other players on both teams (other than the 2 players in the centre doing the kick off) must stand at least 10 yards away from the centre spot where the ball starts off at the kick off. It is a circle so that it can easily be seen where 10 yards is, because 10 yards is the radius.
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It's to make sure the opposition is at least 10 yards away from the ball at kick-off and restarts. This is the same reason for the D adjoining the penalty area.