Give 'em a hug is a pulling move used to improve your pivotal advantage and to get your opponent off balance giving you the opportunity to set up your next move.
In the top photo on the left, Glen has just finished a Say Hello move so his bata and body are now in a good position to give 'em a hug. He slides his bata towards Oliver's hand and re-grasps the bata. The new pivotal is now where the two sticks meet right near Oliver's hand/thumb.
In the second photo Glen pulls his bata back towards himself with both hands taking Oliver's stick with him. This causes Oliver to lose his balance.
This technique can also be used against an opponent fighting with a one-handed grip Irish stick fighting style. (Photos demonstrating this will be added soon.)