The power of lens is measured as reciprocal of focal length. why?

Power of a lens is measured by f/D ratio where f is the focal length and D is the diameter of the lens (or mirror). The ratio gives you the power of an optical device or the light gathering power. Please remember a lens focuses the light. Imagine it as a light funnel. A lens works similar to a funnel. It bends the light rays and bring them to a concentrated spot or the focus, just like a funnel that gathers a liquid and bring it out through a narrow spout. Bigger the diameter of the funnel more liquid it can handle. Same way larger diameter of the lens more light it can bring to focal point. That is how you get f/D ratio.
I hope this makes it somewhat clear?