Hi Brian, I didn't really tackle that in the help file because it is pretty difficult to describe without going into technical details.
Basically it has to do with smoothness.
When 2 curves or surfaces are tangent to one another, that is one level of smoothness.
But there are additional levels beyond that  for example if you have a line and then and arc meeting such that they are tangent, there is still a change in "curvature" between them.
Curvature is basically what radius of a circle a curve resembles at any given point, kind of like how much it is bending at any one point along it. If the curvature between 2 different curves is the same when they meet, that is called G2 or curvature continuity. Tangent is G1 continuity. G3 is a shared rate of change of curvature between the 2 pieces.
The options that say "Blend" mean that instead of a circular arc, there will be a somewhat more organic and arbitrary shaped curve between them, with the given amount of continuity (G1 = tangent continuous, G2 = Curvature continuous, G3 = rate of change of curvature continuous).
One other thing is that the higher types of continuity also require more complex surfaces to be built  tangent requires 4 points for each crosssection, G2 requires 6 points for each crosssection, and G3 requires 8 points for each cross section. So the geometry gets heavier as you use higher continuity.
Things that are curvature continuous have some interesting properties when it comes to reflections  just tangent continuous things will cause a break in the reflection where it crosses the line between the 2 surfaces, while G2 continuous surfaces will have a smoother looking reflection line. So these things tend to come into play a lot more for objects that are highly reflective like car bodies.
 Michael
