Including me.
Sub_Octavian explains what Sigma is / does in the latest Warships Podcast. These podcasts are always worth listening to, interviews with promiment floaty boats players, developers, etc. A few weeks ago he had a retired USN Admiral, who was fascinating to listen to.
In this podcast Kelorn asks Sub_Octavian about Sigma at 6:47 into the podcast. Basically, Sigma influences the likelihood of the shells landing towards the center of your dispersion area.
So it's basically like this:  
(exaggerated example)
On the left we have low dispersion values (Small dispersion area, IE, 'accurate' guns) but low Sigma. You can see that even though all shell splashes are in a smaller area than on the right example (IE, low dispersion) they are spread out more (low Sigma).
On the right is an example of high dispersion (Large dispersion area, IE, 'inaccurate' guns) with high Sigma. You can see that even though the dispersion area is much larger (IE, high dispersion) the shells are more grouped towards the center (high Sigma).
"So what is better then? Low dispersion or high Sigma?"
Neither is 'better' than the other. They work together to create the accuracy of a weapons platform. Lower dispersion with the same Sigma is still more accurate than higher dispersion, higher Sigma with the same dispersion is still more accurate than lower Sigma. The two values work together to make up the accuracy of the guns. Dispersion determines the outer limits of your shell fall area, Sigma influences the grouping within that area.
"So what does this mean for the average player?"
Well, nothing really. Low dispersion still means your shells won't deviate much from your aim point, high sigma still means that the better you are at aiming, the more hits you'll get. It's still a balance between dispersion and sigma values. It just means that we all (Including me, mea culpa) need to stop parroting that sigma is vertical dispersion. It's not, it's grouping.
"So you were wrong then, Lert?"
Yep! I fell hook line and sinker into the 'parrot what everyone else is saying' trap, for lack of evidence written or by experience to thoroughly disprove the common held consensus that Sigma = vertical dispersion. That is wrong, I was wrong.