a jumper wire

A jumper wire is a short piece of wire used to connect two points on a breadboard or between boards, the little bridge that completes your circuit. Some are stiff solid-core wires you cut and bend to lie flat; many are flexible pre-made leads with a small pin or socket on each end, often sold in rainbow ribbons. They carry no special magic; they are simply convenient conductors for hooking things up.

The colours have no electrical meaning, a red and a black jumper conduct identically, but using colour by convention saves you from mistakes: red for the positive supply, black for ground, other colours for signals. They come in male (pin) and female (socket) ends to match headers and breadboard holes. Keeping jumpers short and tidy is not just neatness: long, looping wires pick up noise and add stray inductance that can upset sensitive or fast circuits.

Jumpers are how you turn a schematic into a real wired-up loop. Most breadboard troubles come down to a jumper: one in the wrong row, one not pushed fully in, or a broken wire inside the insulation that looks fine but does not conduct. When a circuit misbehaves, gently checking each jumper with a multimeter's continuity test is often the fastest fix.