Spherical shapes are the most efficient -- they have the smallest surface-area-to-volume ratio of any three-dimensional shape, and are the strongest shapes as well, mechanically speaking. That's why bubbles tend to adopt spherical shapes, because the surface tension pulls them into the most stable form. It's why eggs are spheroid in shape (okay, a lot of them get squeezed when laid, so tend to not be perfectly spherical, but the round cross-section serves the same purpose)
As for spirals, it's a variation on the circle and sphere -- but in this case, it's when the plant or animal needs to increase its volume or surface area. So a fiddlehead fern is tightly coiled into a circle (basically) and then unfurls as it grows to maximize its exposure to the sun. A snail grows over time, but the shell can't expand outward, so the snail forms new shell in an ever-widening spiral to accommodate its larger mass.
That's the naturalistic point of view, of course -- you could ask a mathematician and they might point you to chaos theory, Mandelbrot sets or even the Fibonacci sequence to explain it, but I'm subscribing to Occam's Razor here... keep it simple.