Normally, magnets have two "charges" - a north pole and a south pole - which mean that, overall, the magnetic charge of the magnet cancels out.
Magnetic monopoles, on the other hand, behave more like electrical charge, which have a net positive or negative charge.
Magnetic monopoles were originally proposed by Pierre Curie. Paul Dirac developed a quantum physical theory of monopoles in 1931. Since electrical charges are quantized, Dirac was able to show that the existence of magnetic monopoles is consistent with existing laws of physics.
Many current theories (such as string theory) in physics predict that in the high energy state of the early universe, shortly after the big bang, magnetic monopoles would have existed in nature. If these theories are correct, it would take more powerful particle accelerators to generate the magnetic monopoles.
In addition, it is possible to create effective magnetic monopoles within certain types of materials, so that the north and south poles move freely within the material, instead of in coupled pairs.