A jump ring is a small metal ring with a cut in it: you twist it open with two pliers, hook it through a chain link, clasp or charm, and twist it closed. It is the connector behind almost every necklace and bracelet, and the ring that permanent jewelry is welded shut at.
Which size: chain up to 2 mm takes a 3–4 mm ring in 22–24 gauge; chain of 2–4 mm takes a 4–5 mm ring in 20–21 gauge; chain of 5 mm and up takes a 6–8 mm ring in 18–19 gauge or a soldered ring with a 9 mm+ lobster clasp. Always match the metal of the chain: gold filled with gold filled, sterling with sterling, 14k with 14k.
Jump ring vs split ring: a split ring (a tiny key ring) is stronger but bulky; use it for keychains and heavy charms, and use properly closed or soldered jump rings on chain under 4 mm.

