SG = Specific Gravity = the ratio of the density of a sample to the density of water.
Hydrometers are devices used to measure specific gravity. Distilled water at 60 degrees F has a specific gravity of 1.000. This is your calibration point.
OG = Original Gravity = The specific gravity of the wort after boiling and cooling before pitching the yeast.
FG = Final Gravity = The specific gravity of the beer when fermentation is complete.
The importance is, if you don't take gravity measurements you have no way of calculating your ABV (Alcohol by Volume). You also have no way of knowing when fermentation is complete without SG readings (the general rule is, if you have 3 successive gravity readings spread across three different days that read the same, if the gravity continues to drop fermentation has not completed).