The hanging leg raise with throw down is a more advanced version of the hanging knee raise that utilizes a partner to make the movement more difficult. The partner pushes down at the top of each rep, forcing the lifter to "fight back" with their abs.
Simple way to make leg raises more difficult
Allows you to train in lower strength-focused rep ranges
Easier to find "just enough" extra resistance than by adding static weight
Partner can easily decrease resistance to enable additional reps