SLUGHORN: A Horcrux is an object in which a person has concealed part of their soul.
TOM RIDDLE: But I don't understand how that works, sir.
SLUGHORN: One splits one's soul and hides part of it in an object. By doing so, you are protected, should you be attacked and your body destroyed.
TOM RIDDLE: Protected?
SLUGHORN: That part of your soul which is hidden lives on. In other words, you cannot die.
TOM RIDDLE: And how does one split his soul, sir?
SLUGHORN: I think you already know the answer to that, Tom.
TOM RIDDLE: Murder.
SLUGHORN: Yes. Killing rips the soul apart. It is a violation against nature.
TOM RIDDLE: Can you only split the soul once? For instance, isn't seven—
SLUGHORN: Seven? Merlin's beard, Tom! Isn't it bad enough to consider killing one person? To rip the soul into seven pieces! This is all hypothetical, isn't it, Tom? All academic?
TOM RIDDLE: Of course, sir.
Riiiiight, all academic. Btw, Slughorn really likes that whole "Merlin's beard" expression, doesn't he?
Anyway, this is the big convo that Slughorn had with Voldemort and then tried to cover up. Basically, Sluggy played a pretty big role in teaching Voldemort how to become immortal. Oops. No wonder he didn't want anyone to know what really happened between them.