it's pretty simple (parts of this were "borrowed" from Rhino glossary)

G0 = ends touch, but share no tangency
G1 = ends are tangent (imagine a ball sitting on the floor, the tangent point is where they touch)
G2 = Curvature continuous
G3 = Curvature continuous with a constant rate of change
G4 = Curvature continuous and constant rate of change of the rate of change

jonah