Most of our curve fitting (except for very simple fits, like linear) is done using a non-linear n-dimensional search following methods described in books like Data Reduction and Error Analysis For the Physical Sciences, by Bevington and Robinson.

The uncertainties on the coefficients are the standard deviations of the coefficients as the fitting process takes place. If the goodness of fit depends strongly on a particular fit coefficient, the uncertainty will be low. If the parameter doesn’t change the fit of the line to the points very much, the uncertainty will be large.

Other information on fitting:
How do you calculate linear fits in Logger Pro?
Why don't Logger Pro (or Graphical Analysis) curve fits always work? Why do curve fits sometimes change on opening a file?

The mathematical discussion regarding the uncertainties of fitted parameters in Bevington, or that found in the “Parameter Errors and Correlation” section at https://en.wikipedia.org/wiki/Linear_least_squares_(mathematics)#Weighted_linear_least_squares, is how the calculations are done.

Next, what do the uncertainties mean?

The uncertainties of the fitted parameters are a measure of how strongly the parameter depends on the data. Let’s use the intercept as an example. If the value of the intercept is changed a lot by a little change in the data, then the intercept will have a bigger uncertainty. This is the same as said above, but stated in terms of data points.

Below is a Logger Pro file showing two linear fits of almost the same data; the data sets are just horizontally offset by 100 units. The slopes (and the slope uncertainty) are the same. Changing one of the points a little bit won’t have a big effect on the slope, but in the case of the points out past 100 on the x axis, changing a point will change the intercept by a lot because of that distance from the x=0 line (that is, the y axis).
http://www2.vernier.com/til/3247/intercept_uncertainty_example.cmbl

You can see that Logger Pro calculates the uncertainty of the y-intercept in the two fits very differently. The data out past 100 have a very fuzzy (large uncertainty) y-intercept value because a little change in the data will change the intercept a lot.

Another way of saying that is that the y-intercept is not well determined by Data Set 1.