Wispy describes something that's vague or flimsy. If your explanation of why you didn't help your mom paint the kitchen was weak and didn't help her understand your reasons, you'd call that a wispy explanation.
Wispy can be used more literally to describe things that are physically not very substantial, like the delicate necklace that breaks as soon as you wear it. A person who looks weak and thin could also be described as wispy. A wisp is something flimsy, but in its original meaning, it was a handful of hay or grass — again, something very light.