Electromagnets are made using a coil of wire around an iron core (it can be an iron nail) and letting electricity flow through the wire. Here is a diagram of an electromagnet:

The concept is that the magnetic field around the wire (created by electric current flowing through it) can be strengthened by winding the wire into a coil and twisting it around an iron core.

Here are three ways to increase the strength of an electromagnet:

Increasing the number of coils in the wire

Increasing the current in the wire

Using a magnetic material for the core

Have a look at the Maglev train in the picture below: 

Electromagnets are used in Maglev trains. A computer system controls the current so the train floats 15 cm above the track. The Maglev train is continually pulled forwards because the electromagnets on the tracks are turned on when they are just in front of the train, so they attract the train. As the train moves, the next set of electromagnets on the tracks is turned on and pulls the train in turn.

Electric bells also contain an electromagnet. They are used in most schools.

When the current flows through, the electromagnet attracts the hammer. The hammer hits the gong and the bell makes a sound. The current is turned off and the hammer returns to its initial position.