The season begins with Companions Amy and husband Rory being summoned by The Doctor to the American West, where they are met by two other people. One is River Song and the other is an old government agent who they've never met before. But he tells them that they'll meet again. They do meet a younger version of him, when they travel to 1969. There are these aliens, the creepiest version of "Gray aliens" I've ever seen, that are manipulating events. They are only seen when directly looked at--then people forget they exist, so they are virtually invisible. There's also a disturbing incident in which someone in an astronaut's spacesuit seemingly kills the doctor. But it's hinted that this particular version of the doctor is two hundred years older than the one they've known.
In another episode they encounter pirates, under attack by a Siren. In "The Doctor's Wife", they answer a distress signal and find themselves on a junkyard-like planet, run by some weird individuals. We meet the human incarnation of the Tardis, which gives that machine a completely different perspective. Then, it's on to a future Earth where they encounter a group of humans extracting dangerous chemicals. They've created clones of themselves, to do the most dangerous work, but these clones revolt. And they manage to clone the doctor. In "The Girl Who Waited", Amy is trapped in a quarantine facility--and is stuck there for over thirty years. Can they undo this and get the "young" Amy back? But perhaps the best story is the one which reveals the identity of River Song, who was first introduced in a Season Four episode--and what her relation is to the Doctor, Amy and Rory. It's not totally surprising but it fits very well and adds quite a bit to the context of their relationship.
Season Six is a much darker and grittier this season. It's not my favorite, as it doesn't have the sense of adventure and "fun" the previous season had, but it definitely advances the series into a different direction.