Electricity is a process of the transmission of an electrons group from one point to another. 

That is the definition we find in almost all other books and websites. 

So what are the electrons? 

We must know that the material consists of smaller molecules called atoms that are present in all what is rigid or non-rigid, this atom consists of a nucleus around with rotating electrons, of course the nucleus in turn consists of particles which are the protons and the neutrons. 

We should also know something very important which is that the electrons are negatively charged, the protons are positively charged, but the neutrons do not have a charge. 

Electrons move from one atom to another, this transmission is what generates an electrical current, which runs our devices. 
But when this current is big, it can cause us damage. 
Electrons that can be transmitted from one atom to another are called free electrons, which produce the electrical current. 

So, what is the electrical current? 

The electrical current in its simple sense is a torrent of electrons that run through a conductor. 
From here, other questions fall under this concept 

What is a conductor? Are there some non-conductive materials? And what drives the electrons to move? 

To resolve these questions, we will be first answering this question: 

Are the electrons in the atoms of all materials allowed to move? 

For example: 
Let us assume that we have a copper wire made up of atoms, and these atoms have electrons, so, does the electrons inside the copper wire are moving? 

Are they creating the current? 

The electrons inside the copper wire travel from one atom to another, but randomly. Since they move, they are free, and since they are free then if you give them a stimulus, it can give us an electrical current, so this answers us to the other question, which is that not all materials are conductive, because they are Some substances that prevent electrons from moving from one atom to another, so there are conductive and insulating materials. 

What are the conductive materials? 

Conductive materials are materials that have many free electrons that can be transmitted from one atom to another to produce electricity. 
For example: 
Silver, copper, aluminum, gold. 

What are the Insulating materials?

Insulating materials are the materials that prevent electrons from moving and thus prevent the presence of any electrical current. 
For example: 
Glass, plastic, rubber, wood … 

Why don’t electrons move in conductors on their own so it can be an automatic current? 

For example: 

Let us imagine electrons are water in a tube. If there was no pump, what would happen to the water? 
It will be stagnant or moving a simple movement and we will not be able to take advantage of it, but when installing a water pump, this pump will push the water in the tube in one direction and therefore we will take advantage of it. 
This exact analogy will apply to electrons and electricity. We will replace the pump with a battery which is a store for electrons, once the battery is connected the electrons will be flown from a certain end and the ones in the wire will be pushed in one direction. 
The battery generates a voltage and it is a great source of electrons. 

What is the voltage? 

The voltage is a difference in the charges between the two ends of the conductor that makes one full of electrons and the other poor for electrons. 

In order to further elaborate in this definition we consider that the battery consists of the cathode that is filled with electrons and the anode that is poor for it, therefore when connected, the negative electrons will be separated and then attract to the positive pole, the wire will try to balance this difference and thus this transition will leave an electrical current. 

Note: 

The speed of electrons is always the speed of light, and the voltage difference has nothing to do with its speed. 
The difference is just in their number.