These are called bead stops, they may have other names as well, and they are incredibly useful. You pinch the ends, the coil opens up, you slide a piece of beading wire or thread into the coil and release the ends. They are great at stopping beads from falling off beading wire while a piece is in progress. So if you pick it up, bump it, the cat jumps on it, (you get the idea), the beads stay on.
I design most bracelets and necklaces by taking a piece of beading wire and the beads I’ve selected and work from the center and up the sides. Some beaders design using bead boards or pieces of fleece or towels to keep the beads from rolling around. I like to design on beading wire because I can pick the piece up and see how it looks when it is not flat. Sometimes a design looks great on the table but needs modification when seen at the neckline or draped over the wrist.
Below is a bracelet I am working on and the bead stops have allowed me to see the design on the wrist and at various angles. The little bit of thread tied around the piece? I realized I left a bead off that should go in that spot and that is how I remind myself to add it when I make the finished bracelet.