Question

how are magnets and electricity related?

Answer 1

they are both caused by electrons.
electricity is caused by the movement of electrons.
magnetism is caused by the tendency of a metal to gain the electrons from another metal which ends up futile since metals don't accept electrons (this is only a theory)
also, they are both field forces. electricity can cause magnetism when flowing in a solenoid.

Answer 2

Electric and magnetic fields are intimately related, it's a big subject - here's a very brief summary.

The complete and accurate description of the relationship is given by four equations known as Maxwell's equations.

There are two types of electric charge, positive and negative.

Roughly speaking, electric fields arise from the presence of charged particles, positive or negative, whereas magnetic fields arise when charges are in motion (electric currents).

To answer your question, magnets are materials in which the atomic electrons act like tiny currents circulating in the atoms , giving rise to a magnetic field. In addition, the microscopic currents in strong magnets are aligned with one another, so that all the microscopic magnetic effects add up to give a field that you can easily detect.

Charges experience forces in the presence of electric and magnetic fields (different for each type of field)

Electric fields also arise when a magnetic field is changing in time, and similarly, magnetic fields are produced when electric fields are changing in time. This behaviour can be shown to give rise to what we know as light, which is a closely associated pair of oscillating electric and magnetic fields propagating through space.