The protoconch, or first shell that a snail is born with, grows with the snail as the animal's mantle -- an organ that lines the shell -- releases new shell material that expands the shell before hardening. This shell the snail was born with becomes the center of the spiral.
Newly hatched snails need a calcium-rich diet to help harden their shells, which are initially soft and colorless. They begin by eating the eggs from which they hatched. Most snails are preyed upon when young, before their protective, hardened shell forms, and do not live past the first year. As the snail grows, it continues adding whorls or spirals to its shell; one can use the rings to approximate the snail's age.