A part of the Philosophy of Religion course that's hard to get your head around is Necessary Existence and Possible Worlds. These ideas turn up as part of the Cosmological Argument (especially Aquinas' Third Way) and the Ontological Argument (especially in the version by Malcolm and Plantinga) and finally in Solutions to the Problem of Evil especially in Leibniz's Best of All Possible Worlds argument). Rather than adding to the description on several pages, I'll add some thoughts here.
The idea of 'Possible Worlds' is based on this world not being the only way things could have turned out. The idea of alternative possible worlds is pretty entrenched in DC superhero comics - especially in the adventures of the Flash. However, it plays a big part in Star Trek and even Buffy the Vampire Slayer as well as lots of episodes of Doctor Who. Possible worlds are alternative universes where some significant change made everything turn out differently from the universe we know. The entire plot of Back to the Future Part II depends on this idea.
Possible Worlds illustrate the idea of contingency - that things depend on other things to be the way they are or even to exist at all. For example, it's not difficult to imagine a possible world (let's call it Earth-B) in which you or I don't exist. Our parents married someone else - or married the same person, but under different circumstances - and ::poof!:: we're not here any more (but we are perhaps replaced by someone else who has our name).
Except, perhaps, God.
If God exists, then he'd still be there in Earths B, C and even D (though there would be no people to worship him in Earth D). This is what we mean by saying God has NECESSARY EXISTENCE (otherwise known as ASEITY). If God exists, then he exists in every possible world. Or, put it another way, it's impossible to imagine a possible world in which something could happen to cause God not to exist or make it impossible for God to exist there.
This is because God is non-contingent. He doesn't depend on anything else for his existence or to be the way that he is, so no imaginable change in the surrounding circumstances could make any difference to God.
Leibniz's argument about this world being the BEST of all the Possible Worlds needs more unpacking - in the next blog