A magnet is an assemblage upon which a magnetic field exerts a force. The are two kinds of magnets, permanent magnets and electromagnets.
A permanent magnet is a block of material in which the spin of electrons in the atoms of the material have been lined up. (This can be done in a number of ways, e.g.by placing it in the magnetic field of an electromagnet.) Since moving electric charges can have an effect on the magnetic field, the material becomes the source of a magnetic field. (Normally the spins of the electrons are random, and so they all cancel each other's field out.)