Electrical potentials are generated across the membranes of neurons because:

• There are differences in the concentrations of specific ions across nerve cell membranes

• Membranes are selectively permeable to these ions

Ionic concentration gradients are established by proteins called active transporters, that actively move ions in and out of the cell against concentration gradients. Selective permeability is due to ion channels, which are proteins that only allow certain ions across the membrane in the direction of their concentration gradients. The channels and transporters work against eachother to generate resting potentials and action potentials. In the picture below we have a sodium-potassium pump that actively transports these ions across the neuronal membrane during an action potential.

Using electricity over wires to provide power or information, presents various problems in electrical engineering. A fundamental problem for neurons is that their axons (which can be quite long, like a meter!) are not the greatest electrical conductors. Neurons and wires are capable of passively conducting electricity, the electrical properties of neurons pale in comparison to ordinary wires.

As compensation, neurons evolved a "booster system" that helps conduct the signal over great distances despite their poor electrical characteristics. The electrical signals made by the booster system are known as action potentials. The image below shows the steps of an action potential.

• At -70mV the neuron is at resting potential.

• A stimulus activates the neuron to the threshold level, reaching the threshold level is like pulling the trigger of a gun (like a gun, action potentials are an all-or-nothing event).
  

• So the trigger is pulled and depolarization occurs (ions are moving in and out of the cell to make the neuron less negative/more positive).

• Now we have an action potential, and information from one neuron is passed to the next neuron or target cell.

• Repolarization occurs wher the ions move back to their starting locations and the cell becomes more negative/less positive.

• There is an "overshoot" or a refractory period, where the cell is hyperpolarized (more negative than at resting potential). This refractory period limits the number of action potentials a nerve cell can produce per unit time. This hyperpolarization is why action potentials only move in one direction

• At last the cell returns to its resting potential and is ready to fire again.