A (rather crude) term used often in brown-capping stories. (A brown-capping story is a tale told, often on radio shows like Don and Mike and Opie and Anthony, or in bars, about an unfortunate event in the narrator's life that has to do with untimely BMs. They are usually disgusting, but for some reason funny in a sophomoric and juvenile kind of way.)
As far I can determine, (and I looked long and hard) the phrase was first coined (for this usage - as opposed to the usage described above) by the Greaseman to describe that peculiar event when you have to go number two so badly that no matter how hard you try to hold back, a little bit still pokes out like a prairie dog poking his head up.
Similar phrases for this condition are poking daylight and touching cotton. I'm sure you can infer the meanings of these phrases, so I'll not elaborate.
I don't have any prairie dogging stories (or browncapping stories) myself, although I know of several. Unfortunately, these are not my stories to tell. They involve people I know so holding them up to public ridicule probably wouldn't be a good idea. I will tell you that most involve cops who issue indecent exposure citations, or Walmart bathrooms which need to be cleaned by some poor bastard who works there.