Electro Chemical Cells:

"An electrochemical cell uses energy released from a spontaneous chemical redox reaction to generate electric current. The current is derived from the flow of electrons conducted through metal . . . and the movement of ions in solution, called electrolytic conduction. A battery consists of a single electrochemical cell or a number of cells connected in series." (Fisher, 518) Now I can hear you asking, "what is this stuff that you're talking about?" Well, I'll explain. Here, below, is a diagram of a simple battery that uses a Zinc metal anode, a Copper metal cathode and two different solutions that will provide ions that can travel between the two halves.

Ions:

Ions are compounds or individual atoms that have either lost electrons (been oxidized) making them positively charged, or have gained electrons (been reduced) making them negatively charged.

Anode:

An anode is part of an electrochemical cell made of a metal or alloy that releases electrons, when the circuit is completed, that travel through the electrolyte of the cell, therefore being oxidized.
Cathode:

A cathode is part of an electrochemical cell made of a metal or alloy that accepts electrons produced by the metal or alloy of the anode of a battery when the circuit is completed, and undergoes reduction.
Salt Bridge:

As the Zinc metal is connected to the Copper metal, something occurs. Since Zinc is more easily oxidized than Copper, electrons are lost by the Zinc and transferred through the wire connecting the two half-cells, but only for a split second (hence the reading of 0.00V). During the brief transfer of electrons from the Zinc to the Copper metal, more Zinc ions , Zn2+, are produced in the Zinc Sulphate solution, therefore unbalancing the equilibrium of Zinc ions to Sulphate ions , SO42+. When that happens, the Zinc Sulphate solution is saturated with Zinc ions and won't let any more of the Zinc metal's electrons to be released. Also, happening at the same time in the other half of the cell, Copper ions in the Copper Sulphate solution are being reduced by the electrons from the Zinc metal, forming more Copper metal on the cathode. That process of changing the Copper ions to solid Copper metal unbalances the equilibrium in the right hand side half-cell, also causing the transfer of electrons to stop. The only way to let the reaction continue is to allow the ions to move between both halves of the cell. The answer, something called a salt bridge. A salt bridge can be made of almost any solution of a metal salt, in this example, Sodium Sulphate is used for simplicity.

When the salt bridge is added, negative Sulphate ions flow through the salt bridge from the right half-cell to the left half cell because of the imbalance in equlilibrium. This addition of more Sulphate ions to the left side of the cell restores the right and left half-cells back to equilibrium. This will now allow the reaction that started above to continue on and produce more electrons. The production of electrons continues until a certain amount of the Sulphate ions are left in the right half-cell, a certain amount of Copper ions have been reduced or a certain amount of the Zinc metal has been oxidized. When any of these three things happen the electrochemical reactions are then completed.
Cells:

A unit consisting of a minmum of three parts: a cathode an anode immersed in an electrolyte. This unit will produce a basic amount of voltage, and can be combined with more cells in series (one after another) to make a battery with a voltage directly proportional to the number of cells in the series circuit. So say that one cell will produce a voltage of 1 volt. If there were two of those cells in series, the voltage would be 2 volts.