The secret mission is to investigate possible alien life. You already know this. The novel is constructed in such a way that you already know all the big revelations, and then there's a buildup to the revelation, and then you're like, "I know that already."
Shmoop doesn't know why the novel is set up like this. Maybe Clarke was afraid that if he surprised you, you'd be sad.
Thanks Arthur C.
Anyway, Heywood Floyd pops up again here—not in the middle of space, but on the viewscreen.
He's still boring, but Bowman doesn't notice because Bowman is boring too.
Also, Bowman is facing certain death, so he may be distracted from all the Floyd boringness. You can't really blame him.
So Heywood babbles on about TMA-1 and how it came from aliens and etc.
He says they think TMA-1 was buried and designed to go off when the sun hit it as a kind of alarm; to warn the aliens somewhere out there when someone dug it up.
The signal was aimed at Saturn, so that's why Bowman is headed out to Saturn, and specifically to the moon Japetus—to see if there are superpowered aliens there.