The president is basically replacing the king in a parliamentary system, just like in Germany, Ireland and lots of other similar governments. The president is head of state and possesses limited executive and discretionary powers, chief among them the power to form and dissolve government and his signature is needed to implement laws; the prime minister is the head of government and acts as the chief executive in just about all cases.
While Rivlin is respected as a champion of civil-rights, he does not support the creation of an independent Palestinian state and has been a longtime supporter of Jewish West Bank settlements.
Rivlin has been a vocal supporter of a one state solution; annexing the land and the people living in the territories into the State of Israel.