The pitcher's circle is a a circular area with an 8 foot radius measured from the center of the front edge of the pitcher's plate (rubber).

The pitcher's circle is used at the 8U (Freshman) level to determine when the play has ended, i.e., when the pitcher has control of the ball in the circle play is called dead by the umpire and runners are placed at the correct base according to their position relative to the halfway lines on the basepaths.

For levels 10U (Intermediate) and higher, the pitcher's circle exists as a basis for the "look-back" rule. The look-back rule refers to the requirement that a runner on base not "dance around" while the pitcher is inside the circle, has control of the ball and in no way is attempting to make a play on a runner. For example, when a batter gets a hit and rounds first base, if the pitcher is in possession of the ball within the circle and is not attempting a throw or faking a throw attempt, the runner must either advance towards second base or immediately return to first. She cannot juke back and forth in order to draw a throw. If the runner continues to change direction towards first, then second, the umpire may call her out. Likewise if she stops between bases waiting for the pitcher to throw to a fielder, as sometimes happens between pitches, and the pitcher is in possession of the ball within the circle and not attempting a throw, the runner may be called out by the umpire.

As a general matter with respect to all lines on the field, a player's foot is said to be inside a line when any part of it is on the line. A pitcher is inside the pitcher's circle when both feet are inside the line. For this reason a pitcher standing with both her feet on the line is standing inside the circle.There are no additional rules with respect to anything a pitcher may or may not do while she is inside the circle.

The pitcher is not prohibited from throwing the ball to any fielder from within the circle the way she is if her foot is in contact with the pitcher's plate. There are no rules which prohibit a pitcher delivering a pitch to not step outside the circle but there are prohibitions against her crow-hopping during a pitch. If a pitcher has a long stride which exceeds 8 feet and she ends up stepping outside the circle, the pitch is not illegal due to her stepping outside the circle.

(thanks to girls-softball.com for the bulk of the answer)