Tesla's main claim to fame lay with his invention of the alternating current motor. Tesla believed that alternating current was vastly superior to (Edison's) direct current, but the problem was the lack of a practical motor. Alternating current is practical because of the fact that it can be altered or converted to suit a variety of situations. For example, if the voltage is made quite high, then the current necessary for a specific level of power is very low. This low current then becomes very efficient when sending electrical power over very long wires. (This is the reason why the power lines running across the countryside are at very high voltages.)
Tesla also worked with radio-frequency electromagnetic waves, and despite the claims made by Marconi, actually did invent the idea of Radio as we know it today. (There are numerous patents which bear this out.) In working with radio waves, Tesla created the Tesla coil as a means to generate and receive this form of energy.