Aragorn spent time in Minas Tirith under the name of 'Thorongil', back when Denethor's father Ecthelion II was Steward. Apparently the people of Minas Tirith really liked him, much more than they liked Denethor, and if Aragorn has wanted to reveal himself then, they would probably have made him king right away. It wasn't time yet, though, so after Ecthelion died, Aragorn just left. Denethor resented Aragorn, though he didn't know who he truly was. It's sort of implied that he recognize Aragorn (with the
palantir, maybe) and that's part of the reason why he was angry about Gandalf showing up when he did.
Does that help?
Yeah... I didn't know the background... so, since I'm a detail freak, any detail I learn just builds on the story. That helps explain some of Denethor's anger at Gandalf.