When you turn on the burner, you begin transforming one form of energy (electrical energy) into another (Heat energy). Energy cannot be created or destroyed, it can only change form.
The burner takes the electricity and runs it through a coil that has a very high resistance to the flow of electricity. Frequently Tungsten is used, but other materials have been used as well. The resistance causes the electrical energy to become heat energy. The coil is wrapped in another material that conducts heat, but not electricity so that whoever is using the stove doesn't get electrocuted, while the heat can still reach whatever is cooking.