Galvanic, Voltaic and Daniell Cell Reactions
A galvanic cell is also referred to as a voltaic cell or Daniell cell.  The common household battery  is an example of a galvanic cell.  The flow of electrons from one chemical reaction to another happens through an outside circuit resulting in current.  Current is measured in amperes (A) and is a measure of the number of electrons that flow past a certain point in the circuit at any given moment.

This is a simple redox reaction in which both cells are combined into one.  There is a flow of electrons but not through an outside circuit.
One half of the cell is separated from the other by a porous barrier, sometimes called a semi-permeable barrier or by a physical salt bridge like in the diagram below.  The metal strips are referred to as electrodes and the dissolved salt solutions are electrolytes.

To help remember which electrode does what use the chemist's mneumonic term "REDCAT"
ie.  Reduction(RED) occurs at the cathode(CAT), and oxidation occurs at the anode.
 This is the chemical way of looking at it.
Physics people will tell you the cathode is positive(+ve) and the anode is negative (-ve) and electrons flow from the anode to the cathode through an external circuit.
Do you see the inherent conflict between these two statements.
If reduction occurs at the cathode, then the cathode must have the surplus of electrons, but its' labelled as being positive (+ve).  If the cathode was the surplus then the anode must be deficit in electrons yet it is labelled as negative (-ve).  Why is this???
It comes from the old cause and effect concept.  We are used to looking at the flow of electrons (electricity) that we almost never stop to see what caused the flow to happen.  This is where the science of chemistry comes in.
The reasons behind electron flow don't start with the flow of electrons.  It starts with 2 metals, one being stronger in it's desire for electrons than the other.   (ie. bending trees don't cause the wind to blow either)
Lets see if we can clarify this:
1.    The metal with the stronger desire for electrons; ie the higher electronegativity, is the one that will be reduced. The metal ions in the  electrolyte steal electrons from the metal strip.  This causes the metal ions to become reduced to the metal atom.  The strip of metal, having lost electrons becomes more positive.
2.  The deficit of electrons at the cathode means that there is now a surplus of electrons at the anode. ie. The anode is now negative when compared to the cathode.  (This is the physics point of view)
3.   Electrons flow from the -ve anode to the +ve cathode to replace those electrons lost to the reduction reaction.
4.  As the electron quantity at the anode drops there is an attraction for electrons in the electrode.  As electrons get removed from the electrode, metal atoms in the electrode give up their electrons, becoming positive ions, and these positive ions dissolve off into the electrolyte solution.
5.   If the salt bridge is not there, the cell that is performing the reduction would become very negative, because the negative anion must remain while all the positive cations are being reduced.  The cell that is performing the oxidation will become very positive, because of the formation of positive ions.  Eventually this buildup would stop the reactions since the positive cell would build up such a large positive charge that it would start to become more attractive to the electron flow that the original cathode metal electrode. At the same time the buildup of the large negative charge in the cathodic cell would start to repel or oppose the flow of electrons.   A salt bridge between the two cells allows a balancing of the electrolytes so that this buildup does not take place.  The negative anions from the reduction cell react with the positive cations produced in the oxidation cell neutralizing their charges.
To obtain the overall reaction that takes place in the electrochemical cell, the cell reaction, simply add the individual electrode reactions together. Before doing this make sure that the number of electrons gained is equal to the number of electrons lost. This is a requirement that every redox reaction must obey. Multiply the half-reactions by a common multiple in order to achieve this equal number.
Na+(aq) + e- --> Na(s) (cathode)
Cl-(l) --> Cl2(g) + 2e- (anode)
2 Na+(l) + 2 Cl-(l) + 2e- --> 2 Na(l) + Cl2(g) + 2e- (cell reaction)
Then finish the reaction by cancelling out like terms on either side of the ----->. The overall cell reaction is therefore:   2 Na+(l) + 2 Cl-(l) --> 2 Na(l) + Cl2 (g)