In the film, Hal Jordan, Carol Ferris, and Hector Hammond all recognize each other during the celebratory party. In addition, during the climax of the film Hector implies there is some long history between the 3 of them. I don't recall this being explained at all. Carol and Hal were together when they were younger, clearly, but Hector's history with them is never clarified. In the film, what's the history or relationship between these three?
It is stated explicitly that Hal and Carol have known each other their whole lives. Since Hector's father (the Senator, played by Tim Robbins) also knew Hal and Carol's fathers, I assume Hector grew up with Hal and Carol as well.
This relationship was created for the film, as Hector Hammond was a petty criminal who gained his powers from exposure to a meteor in the original run of Green Lantern, and was introduced to Hal Jordan when they were adults in Green Lantern: Secret Origin.