1) to lead the charge.
2) to take the lead on a campaign, program or project.
3) sometimes used when requesting back-up
etymology: the "point man" is generally the person in charge. The "point guard" in basketball is the player that runs the teams offense. His main objective is to score points.
A) I'm running point on this so I need you to guard for me.
B) This is a difficult project. Who do you have that can run point on this?