The term "slime tube" can refer to the Slime brand of bicycle tire tubes, or it can be used as a more general term for other kinds of tubes that have some form of gel or goopy fluid inside them. Such "slime" oozes out when the tube is punctured (perhaps by glass or a goathead thorn) and can often seal the hole before much air is lost. Generally speaking, these self-healing tubes can only seal very small (about the size of a pin-prick) punctures. They're not very effective for moderate or large glass cuts, punctures by tacks and nails, etc.
The effectiveness of various brands of slime tubes is a matter up for debate, as is their usefulness in road cycling. Mountain bike tires seem to benefit more from slime than do road bike tires, perhaps because mountain tires are usually inflated to much lower pressures than are road tires.