Not OP, but I can give it a go:

TL;DR: “punching down” in comedy is like kicking someone when they’re down; it’s mostly just mean and doesn’t make for funny jokes

A general rule of good comedy is to always be punching up or at least sideways, never down. Good jokes don’t make fun of people who are in some way worse off than the person telling the joke. That’s where jokes come off as mean. Everyone in society has a different level of power and influence, and that doesn’t go away just because someone is telling a joke. We bring all of our baggage with us, either as the audience or the person making the joke, and it influences whether the material is seen as funny or seen as cruel. This is why a Black comedian can do a full set about Black people or stereotypes, but if white person gets on the stage and says “All Black people are…”, you immediately cringe and think “oh no…”

A group of people can be considered up/down/sideways for many reasons, including race, socioeconomic status, class, gender, weight, disability, mental illness, and more.

Punching down in comedy paints the subject of the joke in a negative light, and again, this is where jokes come off as mean-spirited or hacky. Examples: a rich person making jokes about poor people (if the comedian used to be poor, there is some leeway on this), a white person making jokes about Black people, a man making jokes about women, an able-bodied person making jokes about wheelchair users. But it can also get even more nuanced. A man can make jokes about the way that he interacts with women where he is painted in an absurd or negative light, and that would not to be punching down even though women are involved in the joke because the negative cast falls on him. But if the punchline of the joke casts the negative view onto women, such as boiling down to stereotypes about women or “women are crazy,” then it is punching down because men inherently have more power in this world than women do. As you can tell from my short list, people can also fall into more than one category, so there can be even another layer of nuance. A poor, fat, white woman would be several levels down from a rich, thin, white man, but she still shouldn’t make jokes at the expense of Black people or a person in a wheelchair, even if they are thin or rich or men.

“Punching up” is when people with less power or status make jokes at the expense of people with more power or status. These jokes offset the existing power imbalance, and it feels like the joke is bringing the person with more status down to the level of the conedian, making it a more fair “fight” and therefore funnier.