Lightning is a phenomenon caused by very strong Electric Fields in the atmosphere.
When the electric field, , is very, very strong (exceeds ), it provides enough force to rip tightly bound electrons from insulators, creating ions which can then make the insulator a conductor.
Essentially, that is what happens with lightning. Thunderclouds become filled with large amounts of positive and negative charges, which, when accumulated enough cause the electrical breakdown of air, ionising it into plasma, which allows it to carry the charges to the Earth as lightning.