Making jokes at the expense of someone who is of a higher level of power in terms of status or privilege.
Racist jokes, rape jokes, gay jokes, are all punching down, because they are all at the expense of the groups with less power. If you flip them around, and make the dominant group the target instead, it is funny to punch up.
A script that is rewritten with jokes, one liners, and cultural references to make it more appealing to a different audience then the original script was intended for.
The new anime series brought to America has a punch up script made for children.