The cathode consists of lead dioxide (PbO2) and the anode of solid lead. Other commonly used rechargeable batteries are nickel-cadmium, nickel-metal hydride battery, and Lithium-ion batteries. The last of which will be more explained more thoroughly in this article due to its importance. Marcus theory of electron transfer
Marcus theory is a theory originally developed by Nobel laureate Rudolph A. Marcus and explains the rate at which an electron can move from one chemical species to another, for this article this can be seen as jumping from the electrode to a species in the solvent or vice versa. We can represent the problem as calculating the transfer rate for the transfer of an electron from donor to an acceptor 

D + A → D+ + A−
The potential energy of the system is a function of the translational, rotational, and vibrational coordinates of the reacting species and the molecules of the surrounding medium, collectively called the reaction coordinates. The abscissa the figure to the right represents these. From the classical electron transfer theory, the expression of the reaction rate constant (probability of reaction) can be calculated, if a non-adiabatic process and parabolic potential energy are assumed, by finding the point of intersection (Qx). One important thing to note, and was noted by Marcus when he came up with the theory, the electron transfer must abide by the law of conservation of energy and the Frank-Condon principle.
Note the difference in the flow of current and the flow of electrons, this is due to the discovery of the flow of current prior to the discovery of the electron. Benjamin Franklin surmised that the electrical flow moved from positive to negative. The electrons flow away from the anode and the conventional current towards it. From both can be concluded that the charge of the anode is negative. The electron entering the anode comes from the oxidation reaction that takes place next to it. Cathode
The cathode is in many ways the opposite of the anode. The name (also coined by William Whewell) comes from the Greek words κάτω (kato), downwards and ὁδός (hodós), a way. It is the positive electrode, meaning the electrons flow from the electrical circuit through the cathode into the non-metallic part of the electrochemical cell. At the cathode, the reduction reaction takes place with the electrons arriving from the wire connected to the cathode and are absorbed by the oxidizing agent. Primary cell
A primary cell is a battery designed to be used once and then discarded. This is due to the electrochemical reactions taking place at the electrodes in the cell not being reversible. An example of a primary cell is the discardable alkaline battery used in for example flashlights. Consisting of a zinc anode and a manganese oxide cathode in which ZnO is formed.