You encounter Roggvir as you enter Solitude and witness Roggvir's Execution. He is being executed for treason.
Before being sentenced to death for treason, Roggvir was a guard at the Solitude Gates.
During the execution, Roggvir talks about how the High King was not murdered, but rather died in a fair duel.
If you try and save Roggvir, he does not have any additional dialog.
You cannot save Roggvir from the execution. Either the guards will manage to kill him anyway when he escapes, or he randomly dies afterwards (or disappears).
Also note that if you get to close to where Roggvir is during the execution, the guards will assume you are trying to rescue him, and will attack.
Amulet of Talos (After he dies)