In chapter 10, during Eren's flashback, Eren's father gave him a key and told him to embrace the power of Titan transformation if he wanted to protect Mikasa and Armin. His father said that the key is for the basement under their home in Wall Maria where all the secrets would be revealed. I wonder if it's already been revealed in the manga. If it has been revealed, can anybody explain it?
This has not been revealed yet in the manga but there have been further clues than are available in the anime. Please note that this contains major spoilers.
Some Titans can turn back into humans.
This ability can be obtained by eating a human with that ability. Some other titan powers can be transfered in this way. Some lineages of humans have special powers and most of humanity is from a single related lineage. Most of the memories of this family were erased by the "true royal family". One Titan has the ability to hold the memories of some past Titans including the Titan who built the walls and erased the memories. This ability can only be unlocked if a member of the true royal family has that Titan power. As this was said by a member of the true royal family trying to convince his family member to eat the current holder of that power (who wasn't a member of that family) this information is somewhat suspect. At one point in time, Eren's father had this ability (though possibly could not unlock it). In addition, the member of the royal family demonstated the ability to inject himself with a syringe which turned him into a specific titan of his choosing. Eren's father showed familiarity with this family and that ability. In the basement, Eren's father has left some information either about the syringes, unlocking the Titan memory, what he learned via the Titan memory, why he betrayed the true royal family, or simply what we have already learned about Titans and the royal family but what Eren wouldn't have known at the time the key was given to him.
It is also possible (with the way this amazing manga preceeds) that the basement pertains to some secret that hasn't even been hinted to us yet.
This has been revealed now in the manga. Please note that this contains major spoilers.
The basement key... does not open the basement. The basement contains a modest office that looks ordinary. The key opens a hidden drawer in the desk which... is empty. But the drawer has a hidden compartment which contains three books. A book contains a photo of a family. On the back of the photo is a note indicating that this is a photo, not a drawing, and that is proves humanity is alive beyond the walls. The books give Eren's father's life story and how that relates to their current situation. That is being revealled in current chapters.
Updating @kaine's answer... The latest manga (Issue 86) has given further info regarding the key. Major spoilers follow.
The book Eren finds in the drawer opened by the key expands the universe in which the characters live on, saying that not only humanity has not been confined (and on brinks of extinction) but that the ones inside said wall are somewhat exiled from the "main", dystopic society. Eren's father himself was exiled after plotting against the rulers of said society alongside with his original wife, after his original son betrayed the couple.
If you do know what the beast titan is, then the following spoiler (also major, so please be careful) will be an upsetting twist of events.
It has also been revealed that he is the son who betrayed Grisha Yaeger and, conclusively, Eren's halfbrother.