The Basics. One of the oldest civilisations in the galaxy is a bunch of blue dudes who call themselves The Guardians of the Universe. Seriously, that's what they call themselves. They live on a planet called Oa near the center of the Universe, from where they essentially dictate that there must be law and order in the universe. Essentially, they're Time Lords, only they specialise in Weapons of Mass Destruction rather than time travel.
Anyhoo, after a brief, disastrous flirtation with imposing order on the cosmos with an army of android killing machines (not mentioned in the film, but they totally did it. The Guardians are a bunch of reckless assholes, for all of their sitting on big rocks pretending to be Yoda), they came to realise that it was maybe a better idea to allow the peoples of the universe to police themselves, maybe. So they split the universe into 3600 sectors and appointed one suitable individual from each sector to police that sector. These individuals are given Power Rings, which are weapons of immense power and versatility, capable of interstellar flight, firing big bolts of energy, and creating constructs of green energy. All this stuff is powered by the combined willpower of the universe, channeled by the willpower of the user. So if you can think it, you can create it, and the harder you can think it, the more powerful it is.
These guys have nice green uniforms, are called Green Lanterns, and form the Green Lantern Corps. They're this weird combination of 60's optimism, the corps consisting of the most multicultural mix of aliens conceivable (including a sentient planet, a sentient virus, and a sentient mathematical equation), but also a pretty authoritarian stance (the Guardians impose their chosen Lantern on a sector, and you don't get a vote. At least one Lantern in the past has been discovered imposing order on his sector through fascist dictatorship, and this went on for years without the Guardians taking an interest.)
Anyway, the Lantern for our sector, Abin Sur, a purple humanoid bloke, is fatally wounded fighting a being of pure Fear called Parallax, and crash lands on Earth. He instructs the ring to go find a suitable candidate, and it finds Hal Jordan (Ryan Reynolds), a hotshot test pilot, who at least initially is not as full of willpower and lacking in fear as a Green Lantern ought to be. However, the fear creature thing is about to devour the Earth, so it behooves him to become so pretty quick.
As a film, it's really quite good, I thought. I had very low expectations, having heard some dreadful reviews, but I don't think they're all that fair. It's pretty much your standard Joseph Campbell "Hero with a Thousand Faces" monomyth, and in not deviating much from that template, it's a pretty satisfying structure, if not the most original. I've seen some criticism of the film lacking a proper bad guy, the big conflict being against an amorphous cloud of fear and evil. In my view, though, this is where Green Lantern should be. The Green Lantern ring is practically an Ultimate Weapon. If a Lantern isn't up against a big World Eating Monstrosity, then it's a bit overkill. It's all about scale, and scale is delivered.
I would say, however, the film suffers in comparison with Thor. In that the two characters have a similar sort of storyline, and power level, but Thor just being quite a bit better and more fun. Overall, though, not a bad superhero flick, and so what if you're the season's Second Best Superhero movie?