What is a Magnet ?

The simple answer is "A thing that attracts only Iron and other magnetic materials"

Iron is not the only metal attracted to a magnet, Cobalt, and Nickel, and several other metals exibit this strange attraction in varying degrees, but Iron is the most strongly attracted. Many compounds containing these elements are also magnetic, an example is Iron rust.
Magnetic means that it will be attracted to a magnet, Scientists call this property "Ferromagnetism"
The first magnets known occurred naturally in a substance that was called Magnetite, due to it's being discovered on the Greek island of Magnesia thousands of years ago.
Magnetite is a type of stone that is a very high grade of Iron ore.

Magnetite will be attracted to a magnet, but will not always attract Iron.
It is thought that it needs to have been struck by lightening before it
becomes "Magnetized". Magnetized means that it has become a magnet, and it will now attract Iron.
Lumps of magnetite that were naturally magnetized were called "Lodestones".

It was learned that if a lodestone was allowed to turn freely, it would always try to point North.

Lodestones were the first permanent magnets, they had the ability to attract Iron and they retained this ability for a long time.

It was also learned that certain hardened pieces of Iron, if repeatedly stroked by a lodestone, would become magnetized, and would stay magnetized for a long time.
These were the first man-made magnets, and they also had the ability to point North, and to magnetize other pieces of hardened Iron.

Iron and other magnetic materials can also become temporary magnets. These items will act like a magnet when another magnet is brought nearby. But as soon as the magnet is moved away, the temporary magnetic power is lost.

Electromagnets are also temoprary magnets.
Electromagnets are an Iron core surrounded by a coil of wire.
As long as electricity flows through the wire, the Iron will be a magnet, but as soon as the electricity stops, the magnetic power is lost.
Electromagnets can be made very strong and are used to magnetize Neodymium Super Magnets.