Hi Kyle,
Christophe has already provided a good explanation. Sigma is indeed the standard deviation of the Gaussian model used for fitting. It is related to FWHM ~ 2.35 * sigma. I like your suggestion to include the description of columns in our wiki, because it seems to confuse people.
Below is a very poor attempt of a quick drawing :-) Green line represents real data. Red line is a residuum after subtraction of fitted model from the green line. Camera baseline is not shown in the results table, because it's same for all molecules. It is a number user sets in camera settings dialog.

It would be helpful for resolving the issue you reported at Github to attach the zipped file with localizations that causes the problem. If it's possible, do it directly at Github so it's tracked with the issue. Otherwise you can attach it to your message here. If nothing works, you can send it to my gmail.
By the way, Christophe is right that most of the columns are not used. Only x and y are required for merging. However, after the molecules are merged, a "parent" molecule is created and new values of all parameters are recalculated. This is very likely the issue. I'll know more when I see the data.
Best,
Martin