The automatic door bottom is a clever bit of engineering that prevents under-door drafts, without installing a skirt that drags across your floor. Also called an automatic drop seal, it consists of an aluminum extrusion mounted in a dado cut into the bottom of the door. A little brass plunger protrudes from one end on the hinge side.
As you close the door, the plunger is forced inside the assembly, where it triggers the spring-loaded seal to drop to the threshold, sealing the gap. Opening the door causes the seal to retract.
Automatic door bottoms are useful not only for sealing drafts, but also for soundproofing and light control (as in a darkroom).
They're made by companies like Trademark Soundproofing and Pemko. And for those that don't want to, or cannot, cut a mortise in the bottom of the door, they also make surface-mounted variants (that are a bit ugly).