The Department of Mysteries is the part of the Ministry of Magic where they study the great, well, mysteries of life. Ron stumbles unluckily into a room full of brains in jars: a place to analyze the human mind. A Death Eater winds up with a crystal bell jar on his head, a jar that de-ages his head to babyhood and then re-ages it back to adulthood over and over. The jar contains time itself. Then, of course, there is also the veiled archway that kills Sirius. This archway leads directly to death, and once you go through it, there's no turning back. No one knows what is on the other side, though Luna Lovegood and Harry can both hear voices coming through the archway. Perhaps the dead are just out of sight, but still present somehow beyond the archway.
So, there is the mind, time, and death. What is going on with that locked door that cannot be opened, the door that melts Harry's magical lock-picking knife? Professor Dumbledore tells us that this room contains:
... a force that is at once more wonderful and more terrible than death, than human intelligence, than the forces of nature. It is also, perhaps, the most mysterious of the many subjects for study that reside there. It is the power held within that room that you possess in such quantities and which Voldemort has not at all. (36.212)
This power appears to be the weapon Harry holds to protect himself against Voldemort: the power of his own heart. It's essential to the value system of the Harry Potter novels to know that Rowling considers the heart to be stronger than any other force, including the brain, time, even death. Harry is a hero not because he has extraordinary smarts or talent (though he has a good amount of both) but because he has a vast capacity for love and compassion.