There are two games relevant to The Phantom Pain: Metal Gear Solid 3: Snake Eater and Metal Gear Solid: Peace Walker.
Snake Eater, as I'm sure plenty of you will have got tired of hearing by now, is probably the best of the series. It's a wonderful story that even now can bring a tear to my eye.
Peace Walker is the most recent full scale Metal Gear story and is a direct sequel to Snake Eater. It was originally a PSP game which is why the game has comic book style cinematics.
In total the two "movies" last 7 and a half hours, not exactly a brief summary but I'd have to stress that these stories are far more effective when experienced, rather than recapped, Snake Eater in particular. Beyond that if anything's still unclear, ask me! I love the chance to talk some Metal Gear!

The Phantom Pain is just over a week away and my excitement continues to boil over, I know a few of you have expressed some form of interest in the series or said they could never get into it. @Locke, @Circled Square, pretty sure @Everlong said something about it at one point. How about some @Messiah, @Hanley! or @EmperorWu?
I need some more Metal Gear friends.
