The "simple" answer is that hypergeometric distributions are a type of statistics problem. Unfortunately this answer doesn't mean much. The basic example of this problem is the urn problem. Essentially you're looking at a container filled with marbles, some white and some black, drawing some number out, and getting the odds of each combination of black vs. white marbles. Read more on my explanation page.

Update

Curious how the hypergeometric distribution is used in the real world? Check out a real-world use case from Matthew Healy.

Put in any numbers you want for marbles, white marbles, and draws, and I'll show you the (fairly) exact odds of all possible situations occurring. Note that for processing speed concerns (as well as inability to show data nicely), you can't put in very large numbers (max. of 1500 marbles, 1000 white, and 1000 draws). Note also that I'm using my C++ code, not my Ruby code (see below for a link to the source), so this thing should scream.

Number of marbles:
Number of white marbles:
Number of draws:

Want to see my hypergeometric distribution probability calculator source? Great! Click the link, get the source, maybe even read the history of this project.