Electrochemistry is the study of the changes that cause electrons to flow to create electricity. This flow of electrons is created by oxidation – reduction reactions (redox reactions); and these redox reactions are what takes place in electrochemical cells. Chapters 1,7 and 8 of the physical chemistry book tackle this subject in detail, so this post will provide an overview of the topic.
A brief explanation – an electrochemical cell is a device for harnessing the energy of a chemical process to do electrical work. There are two types of electrochemical cells: galvanic (voltaic) and electrolytic. In galvanic cells, spontaneous reactions occur whilst in electrolytic cells, non-spontaneous reactions take place.
Both cells contain electrodes, where the oxidation – reaction occurs. In both galvanic and electrolytic cells, oxidation occurs at the anode (electrons flow from the anode to the cathode) and reduction occurs at the cathode. Because redox reactions in galvanic cells are spontaneous, they are commonly used as batteries.
The energy is harnessed by placing the oxidation and reduction reactions in separate containers joined by an apparatus that allows electrons to flow. By contrast, for electrolytic cells (because they are non-spontaneous), an electrical energy is required to induce an electrolytic reaction.
If a bar of zinc is dipped into a solution of zinc sulphate, some zinc ions (Zn²⁺) dissolve, leaving two electrons each on the metal. This causes a separation of charge and eventually equilibrium is achieved.
An electrical double layer forms, which consists of electrons on the metal surface and zinc ions immediately adjacent to it. At this stage the tendency to dissolve is exactly matched by the tendency of zinc ions to deposit, which is caused by the charge separation. This means that there is a potential difference between metal and solution but it cannot be measured. However, if we can construct a cell using two half-cells, then we can overcome this issue.
Let’s use this example:  zinc electrode in zinc sulphate solution and copper electrode in copper sulphate solution. By preparing two half-cells, these half-cells are designed to contain the oxidation half-reaction and the reduction half-reaction separately. The half-cell called the anode is the site at which oxidation of zinc occurs:

Zn (s) → Zn²⁺ (aq) + 2e⁻

During the oxidation of zinc, the zinc electrode will slowly dissolve to produce Zn ions (Zn²⁺) and enter into the solution containing zinc and sulphate ions.
Likewise, the half-cell called the cathode is the site at which reduction of copper occurs:

Cu²⁺ (aq) + 2e⁻ → Cu (s)

Reduction of copper ions (Cu²⁺) takes place with copper atoms accumulating on the solid copper electrode.
Half-cell reactions however, do not take place unless they are “linked”. For an oxidation reaction to occur there must be a corresponding reduction reaction that is linked. As the oxidation – reduction reaction occurs cations (Zn²⁺) from the anode migrate via the salt bridge to the cathode, while the anions (SO₄²⁻) migrate in the opposite direction. A salt bridge links the two electrolytes, where it allows the migration of ions in both directions to maintain electrical neutrality.
Electrochemical cells give valuable thermodynamic information. Many of the chemical processes occurring around us involve the movement of charged ions in liquids, as well as of electrons in metals. Many corrosion processes arise when aqueous electrolytes are in contact with steel, copper or iron, and battery-powered appliances are common.