cage, fence, pen, enclosure
樊 centers on a bounded space that holds or restricts: a cage, fence, pen, or enclosure.
樊 combines 棥 (a fence-like structure) with 大 (large), suggesting a large enclosure or cage. The exact historical development is uncertain.
The top part 棥 looks like a wooden fence with crossed sticks, and the bottom 大 is a large area. Together they form a large fenced enclosure or cage.
For ハン, imagine a hand reaching through the fence of a cage: hand -> ハン, trying to open the enclosure.