Magnetism and electricity involve the attraction and repulsion between charged particles and the forces exerted by these charges. The interaction between magnetism and electricity is called electromagnetism. The movement of a magnet can generate electricity. The flow of electricity can generate a magnetic field.
Electricity and magnetism are intimately linked: a changing magnetic field will induce a current in a wire and a moving current such as down a wire, produces a magnetic field around it. Maxwell equations are partial differential equations that are often used to mathematically explain this relationship.