Specific Gravity is a number-based reading scale for determining how much sugar is dissolved in your must (future wine). As you add more sugar to a liquid, the SG number gets higher... As fermentation proceeds and the yeast convert said-sugar into alcohol and CO2, the number falls back down.
Water has an SG of 1.000
Alcohol is "lighter" than water, which is how we get SG's in the .990-.999 range
Readings are taken prior to fermentation, during fermentation and after fermentation
Prior to fermentation, the SG is measured to know the 'starting point' for how much sugar there was to begin with. Post-fermentation, it's measured again to determine just how dry the wine has become... A mathematical formula can be used to determine the alcohol content of the wine, by using these two numbers.
(StartingSG - FinalSG) / .735 = .#### = ##.## % ABV
That's the one I use most often, although there are varying formulas, they're all basically the same
Readings are taken during fermentation, to gauge the speed of the fermentation and to make sure it hasnt 'stuck' for any reason