A breadboard is an easy tool for quick prototyping as a temporarily alternative to soldering. The flexibility it offers is ideal to go through iterations fast. A drawback is that wires can come loose easily. Because of this it is not suitable for a final prototype or product. Using matrix board and soldering is a better option in that case.

You use the breadboard to build a circuit by pressing component leads and wires in the holes in the breadboard. By carefully using the connections between the holes in the breadboard, you can make all the required connections from your circuit diagram.

The holes in the small starterskit breadboard are connected like shown below.
breadboard connections

Respectively the holes in the regular breadboard are connected as follows.
breadboard connections

There are breadboards which have continuous power lines (the long ones at the edges), but also breadboards with discontinuous power lines (they separate in the middle). Symbols or lines on the breadboard usually indicate the type you have at hand.