I'm wondering what exactly is shown to the Colonel by Griffin near the end of Men in Black 3 (MIB3)?
I don't remember exactly what the Colonel answered when J asked him what he saw, but it was pretty vague.
He answers with
He showed me how important you are... you and your partner.
So my interpretation is he showed him the truth about J, J's future and his mission:
Young Agent K: You ever wanna see more, I know a top secret organization that can use a man like you.
Colonel: I wish I could.
Here I have the impression that Colonel has also seen his own death.
The film seemed to imply that he was shown clips from J's life; notice that he says J, specifically, is "important", then hastily amends that to being the pair of them. Similarly, he was probably aware that his death is what caused J to grow up as he had, since, as Guy pointed out, he seems aware of his own death.
From what I can recall he said "He showed me how important you were." I'm guessing that he was shown what would happen if J and K weren't allowed to put the Arc Net on the ship.
He obviously showed the man that agent J was his son and that he will die, also that agent k will look over him and that he was going to die.
Also agent k(young) soon realises as well who agent J is