"Post" meaning post-production, which is the editing phase of a production.
This is probably the most hated phrase in digital video production, because when you say "we can fix it in post", it always means that somehow through lack of preparation or simple incompetence you've screwed something up.
Here's a good example that I made recently. At an early evening shoot, I needed to roll tape on a politician in front of a well-illuminated sky. I wasn't looking very closely at the exposure settings, and the automatic gain darkened her face to not overexpose the sky. The original footage looked like this:
Of course, it's completely unusable in this state. Lucky for me, I was able to adjust the gain on the brightness within my video editing program to what you see below.
However, you have to keep in mind that the more digital manipulation you attempt in post-production, the more likely you are to introduce digital "artifacts" to your finished products, which may manifest itself visually as graininess, fuzziness, jagged image edges, even pixelation.
In this image you can see a little graininess, but since it's a quick political video meant to have a reasonably short shelf-life online, it's more or less acceptable. I'm also mad at myself for not doing a better job of leveling the tripod. Look at the horizon to see what I mean.
The finished video is here (the little glitches at the beginning were caused by a faulty tape, not the editing process). Of course, if this was for a paying gig, I'd either reshoot it or refuse to accept payment for it. But seeing as it was simply a project for my political blog and I did it for free, I can live with it.
By the way, the phrase "I can live with it" is probably the second most hated phrase in digital video production!