Explanation for the "puffy vagina" line/joke?

The joke isn't really supposed to mean anything, and was simply something Dan Harmon inserted into the script to make the other writers laugh, but fully expected it to be removed by the network. He forgot the network was Adult Swim, where jokes of this nature are pretty much allowed, and the showrunner is Justin Roiland, who's totally fine with this type of humor and is known for worse.

From an Ask Me Anything on Reddit:

When you write a script for TV, there's a schedule. The job isn't done when the script is "finished," it's done on Wednesday, finished or not. You acquire a discipline in TV writing of working in passes.

I had the script up on a big TV in the writers room and I was going through it, doing my pass, and I put the puffy vagina line in there. I thought, hey, this'll make the writers laugh, and then we'll be done with the script, and we'll send it to the network and they'll know it's a placeholder and they'll say "of course you have to change that" and the writers will say, "okay, let's change that now."

What I failed to realize is that the network is Adult Swim and the showrunner is Justin Roiland. So now we have Rick saying that this girl has a puffy vagina. And your question, which is totally valid, is why does Rick know that.

Why indeed. And, I mean, it's canon, so I'll answer.

I think Rick heard a rumor. I think Rick was working really hard on Pirates of the Pancreas and he'd make routine trips to the inside of Ruben, and I think, you know, in the break room, people talk.

Justin Roiland chimed in with his own answer in a comment:

I think he had an up close and personal face to skin experience with Annie's puffy vagina. He just doesn't like em puffy man. Me? I'll take em however I can get em! (JK, I have pretty high standards)

As an actual real life woman, if anyone has ever seen a vagina you see how flat the labia can be on a woman but some women have more fat in that area, creating ''puffy'' vaginal lips/labia.

I thought he might have meant a real condition called vulvadynia. It's a condition when the birth canal clamps shut tight when the vagina muscles contract simultaneously. It is reputed to be caused by sensitivity to dietary oxalates.