Well a potato is a tuber and garlic is a bulb, but a dahlia is technically a tuberous root - a weird looking thick and fleshy root, connected to a piece of stem material, that stores energy over winter, so that it can sprout back to life as the next growing season begins.
However, all around the globe, gardeners, farmers & breeders alike, simply call them tubers, probably much to the irk of botanists and prigs.
In most areas of the U.S. dahlias are not suited to being left in the ground over winter. Here in the North West the winters are wet and dahlia tubers can occasionally rot, elsewhere it gets too cold and the dahlia tubers are killed. In areas with mild, dry winters, dahlia tubers can be left in the ground all year... however you may want to dig them up and divide them from time to time.
Dahlia tubers require an 'eye' to sprout a new plant. These eyes are located on the stem tissue at the top of the tuber and are typically hidden while dormant over the winter, only to swell and appear as little white or pink bumps as the warmth of spring set in. Tubers with no eyes may develop roots, but no plant will emerge.