What exactly is the flagstick, and why is it important?
You may see the flagstick from the tee, or in the fairway. In both instances and once you reach the putting green, the flagstick indicates where the hole is located.
So, can I putt with the flagstick still in the hole?
Yes, as per Rule 13.2, there is no penalty for leaving the flagstick in. You may do this from anywhere on the golf course including when your ball is on the putting green.
You are allowed to putt with the flagstick in the hole, and there is no penalty if your ball strikes the flagstick. If the flagstick is attended or removed while you make your stroke, it can be moved out of the way while your ball is in motion. If you decide to leave the flagstick in the hole, it must be left in position from the time you make your stroke until your ball comes to rest.
Keep in mind, if you opt to have the flag "tended" and if the player tending the flagstick deliberately fails to remove the flagstick and the ball strikes the flagstick, that player incurs the general penalty (2 strokes) and the original stroke does not count and the stroke is replayed from the original spot (Rule 13.2b(2))
Watch the video below to learn more about the flagstick and how it applies to the Rules of Golf.