Plantinga believes his modal version of the ontological argument avoids Kant's criticism that "exists" is not a predicate.
Modal logic concerns possibility, probability, and necessity. All modal truths are necessarily true. E.g., it is possible that a unicorn exists. The statement It is possible that a unicorn exists is necessarily true. If it were not so, then it would be not possible that a unicorn could exist. But that is absurd.
1. There is a possible world where maximal greatness is instantiated.
2. Therefore, God exists
Maximal excellence: A being is maximally excellent if, in some possible world, a being has omniscience, omnipotence, and moral perfection.
Maximal greatness: A being has maximal greatness if it has maximal excellence in every possible world.
The idea of a maximally excellent being is coherent. The idea of a maximally great being is coherent.
So, both a maximally excellent being and a maximally great being are possible beings. That is, there is a possible world where a maximally excellent being exists. And, there is a possible world in which a maximally great being exists (our premise 1).
Premise 1 is necessarily true.
If there is a possible world in which maximal greatness is instantiated, then a maximally excellent being is instantiated in every possible world.
Our world is a possible world. (That which is actual is also possible).
Therefore God exists in our world (and every possible, to include actual, world).