Power still rests with the Supreme Leader Ali Khamenei, who can wield it directly or indirectly with his control over the Revolutionary Guard, the judiciary and the intelligence services through hand-picked loyalists. That's where the power was and will be.
Then there is the Guardian Council of 12 experts of Islamic law who not only have to approve candidates for elected office (dozens were barred in this election, notably those who are seen as " the opposition"), but also has veto power of any parliamentary bills considered to bei in violation of the constitution.
The President has limited power,( subject to the above), whether it be political, social, educational, media etc. He represents the country aboad but again he can be and usually is reined in by the above who also control foreign and defence policies. Thus, whether it be the nuclear programme or the USA or the UN sanctions or Israel or Syria or Hizbollah etc. , it is the Supreme Leader and the Council of Guardians who are in charge.
There is a parliament (Majlis) of 290 members elected every 4 years, who can set economic and social policies but again subject to the "loyalists" of the Supreme Leader. Then there is the "hand-picked" Expediency Council which mediates between Guardian Council and parliament. They are more an advisory body to Khamenei and do his bidding. Finally there is the Assembly of Experts, an elected body of 86 clerics whose role is to oversee the supreme leader's performance. but really they are there to select a successor after his death, because the Supreme Leader ( at least so far), remains in his position until he dies.
The election of Rowhani may bring some hope to his followers, and a new face/ voice to the world, without the bombast of Ahmadinejad, but like former president, Rafsanjani (another so-called moderate, who was prevented from running this time), he may "tinker around the edges" but will not be able to make any changes that are not approved by the Parliament, the Guardian Council and especially the Supreme Leader. The next few weeks will be interesting, for it will indicate how much leeway, Rowhani is allowed.
It is obvious, or should be, that the Guardian Council and teh Supreme Leader are not too bothered by his "moderation". They after all, allow him on the ballot. He is not an outsider and he will not shake things up or else he is "Gone". Plus ca change, plus c'est le meme chose'?