All matter is made up of atoms, and atoms are made up of smaller particles, called protons (which have positive charge), neutrons (which have neutral charge), and electrons (which are negatively charged). Electrons orbit around the center, or nucleus, of atoms, just like the moon orbits the earth. The nucleus is made up of neutrons and protons.
Some material, particularly metals, have certain electrons that are only loosely attached to their atoms. They can easily be made to move from one atom to another if an electric field is applied to them. When those electrons move among the atoms of matter, a current of electricity is created.
This is what happens in a piece of wire when an electric field, or voltage, is applied. The electrons pass from atom to atom, pushed by the electric field and by each other (they repel each other because like charges repel), thus creating the electrical current. The measure of how well something conducts electricity is called its conductivity, and the reciprocal of conductivity is called the resistance. Copper is used for many wires because it has a lower resistance than many other metals and is easy to use and obtain. Most of the wires in your house are made of copper. Some older homes still use aluminum wiring.
The energy is really transferred by the chain of repulsive interactions between the electrons down the wire – not by the transfer of electrons per se. This is just like the way that water molecules can push on each other and transmit pressure (or force) through a pipe carrying water. At points where a strong resistance is encountered, its harder for the electrons to flow – this creates a “back pressure” in a sense back to the source. This back pressure is what really transmits the energy from whatever is pushing the electrons through the wire. Of course, this applied “pressure” is the “voltage”.
As the electrons move through a “resistor” in the circuit, they interact with the atoms in the resistor very strongly, causing the resistor to heat up – hence delivering energy in the form of heat. Or, if the electrons are moving instead through the wound coils of a motor, they instead create a magnetic field, which interacts with other magnets in the motor, and hence turns the motor. In this case the “back pressure” on the electrons, which is necessary for there to be a transfer of energy from the applied voltage to the motor’s shaft, is created by the magnetic fields of the other magnets (back) acting on the electrons – a perfect push-pull arrangement!