Cells, often incorrectly used interchangeably with batteries, have three parts. There are two electrodes (electrical terminals) and an electrolyte (chemical medium). The electrodes are called the anode and the cathode and are separated by the electrolyte, which enables the electrical charge to flow between them. The anode is the negative terminal while the cathode is positive. These are the parts that are connected to the electrical circuit.
When multiple cells are electrically connected, the resulting combination is called a battery. A normal cell has a voltage of 1.5 volts. By connecting multiple cells you increase the voltage. As such, batteries will generally be some multiple of 1.5 (3V, 4.5V, 9V…).
Once they are connected, a chemical reaction takes place. Because opposites attract, this reaction causes the (negatively charged) electrons to build up at the (positively charged) cathode, which results in an imbalance of electrons. The electron’s like to rearrange themselves to balance out the imbalance. The only place for the electrons to go is through the electrolyte to the cathode. However, it is only when a conductive material (metal wire) is connecting the anode and cathode, that the electrons can move through the electrolyte. By completing the circuit, the wire allows the electrons to balance themselves completely by allowing them to flow from the cathode to the anode through the electrolyte as well as back to the cathode through the wire.
Being that the wire is connected to a light bulb or other device the electrons will, while flowing through the circuit, power the light bulb. Let me point out that it would be if you would not have a device (light bulb) in the circuit, this is a short circuit and will cause, at the very least, sparking (not recommended).