Stolons are specialized stems, often called runners, that grow at or just below the soil line.
Stolons are one way a plant can regenerate. Stolons send new roots down at the nodes and new stems up at the buds. Strawberries and potatoes grow from stolons.
New plants produced by stolons are clones of the parent plant, or genet. Some turf grasses, such as St. Augustinegrass and various bent grass species, grow from stolons. Other grasses, such as Kentucky bluegrass and red fescue, grow from rhizomes. In either case, this growth habit makes it possible to grow new plants from plugs. It is also why some weeds are so difficult to eliminate.
I hope this information inspires you to grow more of your own food. You can ask your garden questions on my Home page.