We first hear about Delbert Grady as the crazed former caretaker who butchered his family and killed himself while looking after the Overlook Hotel. He just seems like a (super) creepy dude from the past until he actually shows up dressed as a Butler in front of Jack.
Jack recognizes him the moment Grady tells him his name, but Grady insists that Jack is the only caretaker of the hotel… and always has been. That said, Grady also has some advice to give Jack about how to deal with his family at the Overlook. When his own daughters tried to burn down the hotel, Grady says,
"But I corrected them, sir. And when my wife tried to prevent me from doing my duty I corrected her."
By "correct," Grady means "kill," and he wants Jack to do the same thing to his family. Yikes.
On top of his ghostly ability to appear and disappear, Grady is also able to detect when little Danny Torrance is using his special powers to call Mr. Hallorann to the hotel. As he tells Jack,
"Your son has a very great talent. I don't think you are aware how great it is, but he is attempting to use that very talent against your will."
We also find out that Grady is in agreement with a bunch of other spirits in the hotel that Jack should kill his family. Hey, whatever happened to friendly ghosts? Why can't this hotel have at least one Casper?
When he expresses his doubts about Jack's abilities, Grady says,
"I and others have come to believe... that your heart is not in this, that you haven't the belly for it."
We're not exactly sure why Grady wants Jack and his family dead, but it might have something to do with wanting their spirits to live inside the Overlook forever, and the only way this can be accomplished is if they die in the hotel. Or they might just be psychotic. You be the judge.