I think some people could read the title and come away thinking that Medvedev, a long time lapdog of Putin, is resigning in protest. He's not.
Those who are cynical of Putin in Russia see this as a way to keep Putin in power without having to rewrite the Russian constitution's limits on presidential terms. Currently, a Russian president can only serve for 2 consecutive terms, which Putin did and then he essentially appointed Medvedev as president for one term (opposition to Medvedev were widely jailed or given trumped up charges so they weren't allowed to run), created the position of Prime Minister which Putin occupied for one presidential term, and then Putin returned as president after Medvedev served one term. The idea this time around is that by Medvedev resigning the post of Prime Minister, Putin could remake it as an influential position in the country, his allies in Parliament would then "Democratically" vote him in as PRime Minister when his final term as president ends, and some other sinecure would move into the position of President. Should there actually be a legitimate challenger in the presidential position who is not one of Putin's allies -- which is a near impossibility to think of today -- the Prime Minister would end up having more influence than the President.
How can Russians tolerate this?
About 100 years of government-orchestrated disinformation, a perpetually nihilist world view espoused by the Russian government, and the factual reality that ordinary life in Russia under Putin has been better than ordinary life in the Soviet Union and arguably under Yeltsin as Russia transitioned into a modern economy (this is important too, while elections are rigged in Russia, Putin
is popular because the older generation just has to look back 35 years to bread lines and empty store shelves, the younger generation just has to look back to the chaos of the 1990s, and the youngest generation only has government nihilism). But, chiefly those first two. For about 20 years in Russia Putin has crafted a reality where there is no truth; it was the mindset of the KGB in the Soviet Union, the mindset of the newly rebuilt FSB once the Soviet Union collapsed, and he's spread that throughout Russia over the last 20 years. Garry Kasparov tells the anecdote about how Russians in the Soviet Union read the newspaper back to front, because the back pages were where real truth was reported, and the front pages was the official Communist Party propaganda. Today, nobody bothers to read the newspaper because there isn't a single version of the truth presented in it.
For what it's worth, Donald Trump runs his White House press briefings similarly. It's not just that Trump's press briefings are regularly filled with lies, it's that tomorrow's lies will undermine the lies from the day before, with the goal being that nobody knows what to believe and nobody thinks that there's any valid truth. The goal is nihilism.
*EDIT*
I wanted to add a caveat to my point about how ordinary life is better in Russia than it was in the Soviet Union and under Yeltsin. It is better if you are an ethnic Russian, and if you are not an ethnic Russian then life is not better and worse in different ways. I don't want to give the impression that, say, Chechens have a better life in Russia today under Putin, or any other ethnic and religious groups in Russia that are frequent targets of police violence.
