Dumbledore is in his office looking over some weird objects. Wait, isn't that Tom Riddle's diary, which was destroyed in Chamber of Secrets?
There's a knock, and Dumbledore drops a ring inside the big hole in the diary and shuts both objects up in a drawer. Nothing to see here, just doing some quick desk cleaning.
Turns out it's Harry, responding to a message from Dumbledore.
After some "chit-chat," they get down to business: Dumbledore wants to use the Pensieve (that bowl that looks kind of like a magical birdbath, where he can drop and then view memories) to take Harry into a moment in his past.
It's a biggie: the day Dumbledore first met Tom Riddle (a.k.a. Baby Voldemort).
Harry and Dumbledore dive into the Pensieve, and we see Dumbledore (complete with throwback hairstyle and scarf) visiting Tom Riddle at the orphanage.
The woman in charge tells Dumbledore that Riddle has been having trouble with other kids…lots of "nasty" stuff seems to happen when he's around. Color us shocked.
Dumbledore explains he wants to take Tom to Hogwarts. Tom has been living in the Muggle world up to this point in his life, so this is probably the first time that someone has acknowledged that he's, er, different (and boy, is that an understatement).
Dumbledore tells Tom that he's a wizard.
Tom asks him to prove it, and Dumbledore does—by lighting Tom's closet on fire and then drawing Tom's attention to something he (magically) knows Tom stole.
Aaaand, flashback over. Harry and Dumbledore leave the Pensieve, and Harry asks if Dumbledore knew then about what a bad dude Voldemort was going to become.
Now, Dumbledore's recent adventures with Harry might seem a little random. Why did he take Harry to visit Slughorn? And why show Harry this memory of Baby Voldemort?
Well, Dumbledore sheds a little bit of light (never too much) on those matters at this point: Dumbledore definitely seems to want Harry and Slughorn get to know each other. Dumbledore wants something from him (we don't know what yet, though), and it looks like Harry is going to be in charge of finding it.