What does “pregnant pause” mean?

Solution 1:

A pregnant pause is a pause that builds up suspension in the listener/viewer, for a greater dramatic (especially comic) effect of what follows after the pause.

Edit: Merriam-Webster has this:

 3. rich in significance or implication <the pregnant phrases of the Bible — Edmund Wilson> <a pregnant pause>

Wikipedia has this bit specifically on comic timing:

A pregnant pause (as in the classical definition, "many possibilities") is a technique of comic timing used to accentuate a comedy element, where the comic pauses at the end of a phrase to build up suspense. It's often used at the end of a comically awkward statement or in the silence after a seemingly non-comic phrase to build up a comeback. Refined by Jack Benny, the pregnant pause has become a staple of stand-up comedy.

Solution 2:

I've always taken it to mean a pause that engenders an expectation ("pregnant" = "expecting") for the listener. This as opposed to a pause to let the listener reflect on what was just said, a pause for the speaker to catch his breath, a pause for the speaker to find the right words, etc.

It could be used in telling a joke, making a sales pitch, storytelling, or as a form of emphasis that can only be described as legen...

(wait for it)

...dary!!!

Solution 3:

I think that pregnant in this case has the meaning of heavy, loaded, gravid, with burden.

(In most slavic languages the word for pregnant is derived from "with burden")