Michonne gives her an ultimatum: either come with her, or stay in Woodbury without her.
T-Dog, Lori and Beth are watching this from the car, and a walker's arm was blocking part of the window they were looking through, not allowing them to see that Andrea had indeed killed the walker, so they assume that she is dead, and they drive off.
She has increased her gun-wielding prowess and believes that she is now able to dispatch threats from a distance with proficiency.