Wires help us connect electrical components into circuits. A wire essentially is any length of conductive material that can join electrical components. There are many types of wires with different gauges, connectors, and internals. For breadboarding, you can use male jumper wires to connect the rows together. On a printed circuit board, there are traces, which are essentially copper wires connecting components.
Sparkfun has a great tutorial on working with wire if you want to know more about them.