Unlike hermit crabs, which move into empty shells as they grow, a snail keeps the same shell its whole life. It simply keeps building.
The work is done at the shell’s opening. A layer of tissue called the mantle lays down new material, mostly calcium carbonate, around the edge. Each addition is a little wider than the last, and because the snail’s body is coiled, the shell coils with it. The spiral you see on a snail’s back is a record of every stage of its growth.
That is also why snails need calcium. Gardeners sometimes find them scraping at chalky soil, old mortar or eggshells left in the compost. They are not being strange. They are gathering building supplies.
The fine lines that run across a shell are growth lines, much like the rings in a tree. A pause in growth, such as a long dry spell or a winter spent sealed shut, often leaves a thicker line behind.