In colloquial terms, a "roast" is also a special event in which a famous or important person has a dinner held in his or her honor. The person doesn't have to be world-famous, local "roasts" of local celebrities are also a "thing".
The reason it is called a "roast" is that speakers are invited to a podium to give a small speech in which they "roast", or comically mock the guest of honor. There is a designated Master of Ceremonies referred to as a roastmaster. The Friars Club of New York City started the whole shebang in the early 1900s, and the format was popular during the early 20th century.
They're less popular these days, we've moved beyond a world in which the likes of Don Rickles was considered a draw for walking through an audience mocking people's ethnicities, handicaps, and personal eccentricities - well, considering the election of Donald Trump, maybe not. But the American comedy channel Comedy Network have released a series of specials in which the likes of Charlie Sheen and Cheech and Chong have been heckled by a gallery of D-listers for the dubious entertainment of the masses.
The "rules" of a roast is that no matter how evil, how cutting, or how thoroughly unpleasant the jokes are at your expense, you're supposed to demonstrate a certain stiff upper lip and strength of character and laugh along with everyone else. In some instances "ground rules" are set in terms of where lines are drawn, especially when the target is someone who is known to harbor a grudge, or have friends who do. But to give an idea of how these sorts of things work, a roast of William Shatner had to actually suggest an agreement with the comedians in question. To not mock the fact that Shatner was considered a suspect at one point when he came home and found his wife floating face down in a swimming pool. You'd think that that "line" was common human decency, but to these sorts of folks making a joke to someone's face about their spouse being dead is funny, am I right?
You are also expected to take some shots at the other members of the panel, as well. To "spread around" the insult and show it's all in good fun.
To give you an idea about the sorts of comedians who relish this gig and the sort of event it is, Jeff Ross once appeared dressed as Joe Patermo in coaching gear - because making fun of the systemic rape of young boys over decades is clearly in good taste. Lisa Lampanelli shows up with her only "joke" - to remind us yet again that she sleeps with black men, as if it's in any way scandalous or "edgy" to do this in 2016.
Occasionally, with the right comedian and the right target, you can get some great humor. Mike Tyson, who was on one panel, had it remarked about him "of all the faces you (messed) up, you (messed) up yours the most!" with respect to his pre-fight facial tattoo. Hulk Hogan was told he was there because they needed "a dumb blonde with big (breasts)." To which he cheerfully did that bodybuilder thing of flexing one pectoral muscle at a time with a huge grin.
Then there are moments like when Amy Schumer took a shot at recovering drug addict Steve-O. Passing it off as genuine condolences for the loss of his close friend Ryan Dunn who died in a fiery car crash - she started by saying he probably wished it had been him that died instead of his friend. And then twisted the knife by saying "so do we." The audience booed her and it became a minor scandal of sorts for her, as Steve-O's reaction clearly showed that he hadn't sufficiently grieved the loss to see any humor in it.
At the end of the dinner, the roastee does get the "droit de réponse" to stand up and fire back at the abuse he or she has received all evening, and add in his own shots at the assembled "roasters", who are expected to take the jabs with equal grace and diplomacy. But realistically it's like a game of "Roshambeaux" - "I kick you in the nuts, then you kick me in the nuts, so it's cool cause we're even". How about NOT kicking each other in the nuts, and simply enjoying a half decent meal?