Capture points are objectives which can be taken.
In the action game they are normally centered around a radio or equivalent broadcasting equipment, where the soldiers capturing the point send a report back to HQ reporting that they are in control of this area.
Capture points with a star shaped background on the map are the mission objectives on this map. Capture points must be captured in a specific order, as they are locked until the previous point has been captured.
When capturing or defending an objective you will notice a number under the objective icon. The blue number displays how many friendly players are capturing the objective, while the red number shows how many enemy players are present.
Having more people at an objective will let you capture it quicker as compared to when capturing it on your own.