What exactly happens during "Puff-Puff"?
While playing Dragon Quest 11, I bumped into a woman who suggested to do a "puff-puff" to me in Gallopolis. I agreed, she took me (alone) to a room, then the screen went dark and when light was back, turned out the "puff-puff" was done by a huge muscular man with a helmet.
It didn't cost anything, and I have no idea what really happened there. My assumption was that it's kind of massage, but quick Google search showed mix results, including some old ongoing meme.
Even the wiki page doesn't give much details, e.g. the screenshot of something done with slimes is from a different game (not XI) and surely it's not a combat skill.
So, any details what's going on during the "puff-puff" time?
Solution 1:
This is something that's a bit of a running joke throughout the whole series. As far as I know, we are never really shown what happens during the puff-puff in Dragon Quest. It's always left to the player's imagination and surely some sort of innuendo.
Note for completeness sake, the general consensus is a "puff-puff" involves a woman putting the recipient's head between her (large) breasts. But again this is never explained in-game, and we don't know if this is really what is being referred to. And clearly in many cases it isn't - as is the case with the scene in question.
The particular scene you're referring to is a reference to a similar scene in Dragon Quest III. The main character is offered a puff-puff by a dancer in the street. If accepted, she leads the character to her house and takes him upstairs alone. She instructs him to sit on the bed, turns out the light, and the puff-puff begins. Whatever is going on really feels good! But when the lights come back on you see her father next to the bed, who we learn was...massaging the characters shoulders. Hmm, not quite what we expected.
Here's a video of that scene (English ver.) along with a pretty good explanation of it:
Solution 2:
While Lee's answer is quite correct in that in the games itself it can vary and mostly used for comedic effect with things like slimes (DQ8) and sheep (DQ9), this is a well-known trope with the busty-types in Japanese media, and usually associated with what they tend to catalog as 'Onee-kei' (お姉系), or big sisters. It's probably why you see dancers and such kind of characters use the term, but not limited to (I think it can be used as a skill by male characters, too.)
Probably thanks to Toriyama in Dragon Ball (NSFW?) and Dragon Quest, it's a type of onomatopoeic word now in common parlace taken to mean 'the soft sensation of squishing someone's face in between two soft mounds', e.g. breasts.
Its usage is not limited to relatively safe video games and anime, so keep that in mind if any other research is to be done. You can see illustrations of the act in Pixiv's entry for the tag, of course, these can be NSFW due to the nature of the topic.