Graves tells Kaladin and Moash that with Elhokar out of the way, Dalinar would become king and be much better for Alethkar. Obviously Graves isn't totally truthful with them, he is working for the Diagram and wants Dalinar to be king in hopes he becomes the Blackthorn, the warlord, and provides no real competition to Taravangian in becoming king of everything. However, in the scene when Kaladin faces down Graves and Moash, Graves makes a comment on how it was too late, and he just had to keep Kaladin away from Dalinar, presumably so Szeth could assassinate him. Then the last we see of Graves, he is talking to Moash and says
I thought for sure my interpretation was correct, that if we removed Elhokar, Dalinar would become our ally is what is to come.
How would Dalinar become their ally if Graves was purposely keeping Kaladin away from Dalinar so Szeth could kill him? Is Graves lying to Moash there? That part I never fully understood. It seems as though Graves understands Dalinar is going to be assassinated, yet from what he says to Moash at the end he seems to expect Dalinar would not have been killed.
Graves is supposed to (though people missed this, so perhaps I didn't do it well enough) indicate that the Diagram is not simply one group, following Taravangian. They follow the diagram itself, not him, and some think his interpretations are wrong.
Graves was ordered to remove the Alethi leadership entirely--though Taravangian was sending Szeth after Dalinar (the more dangerous one) and Graves was to remove Elhokar. Graves, however, interpreted the diagram differently. He thinks that Dalinar cannot be killed by Szeth, or anyone, and is hoping to remove Elhokar, have Dalinar step up, and help them. He has passages of the Diagram that indicate, to him, this is the natural outcome of removing Elhokar.
The actual passages, and what it is they're trying to accomplish in specific, has yet to be revealed in full.