Stolons are commonly known as runners. They're horizontal plant stems that can for roots and new stems at the nodes or at the ends. It's a form of asexual reproduction which sometimes leads to stands of one type of plant.
Strawberries have stolons. I've got a few strawberry plants on my balcony, maybe all grown from the same individual. They have stolons hanging down from the pot which form new leaves every 15 cm or so and would root if I put them in water. If a new plant is set up, the stolon can be cut from the mother plant and the new plant will continue living, relying on itself. It is, however, genetically identical to its mother and thus, even plants that produce stolons need to reproduce sexually or they would stop evolving and eventually get wiped out by something they can't evolve a defense to.