Other forms: parabolically
Something that's parabolic either relates to a simple story used to teach a moral lesson (a parable) or resembles the U-shaped curve found in math and physics (a parabola).
If your grandfather's stories always end with him saying, "And the moral of this story is..." then you can describe his stories as parabolic. They are parables, in other words, tales that try to teach a moral or religious lesson. Another way to use the adjective parabolic is to mean "like a parabola," or a mathematical curve on a graph. The Greek root of parabolic is parabolikos, "figurative," from parabole, "comparison or parable," or literally "a throwing beside."