this war is actually against NATO, not specific to Ukraine at all.
For what it's worth, this is roughly what I got from Putin's two recent addresses. I've italicised it to show it's not necessarily what I believe, just what I understood Putin to be saying.
Russia's main motive in this conflict is to prevent further militarisation of Ukraine. They must not join NATO or allow foreign military bases & missile sites on Ukrainian soil, as per the Ukrainian constitution and the agreements made with Western powers in the early 1990s, which were the basis on which the Russians withdrew from the territories they occupied post WW2. Putin contrasts the Russian withdrawal with successive waves of NATO aggression, which means the alliance is now at the Russian border. He talks about the millions of lives taken in the Great Patriotic War and says Russian cannot pay such a terrible price again.
Putin says Ukraine's stated ambition to acquire nuclear weapons is unacceptable. Ukraine already has extensive nuclear power infrastructure and old Soviet launchers, so Putin says he cannot delay acting, as they could obtain nuclear capability very quickly.
The second reason he gives is to eradicate the neo-Nazi militias. He frames the intervention as a human rights mission to defend the ethnic Russian minority, who have had their language made illegal and suffered various other insults, including the shelling of the regions where they predominantly live. Putin describes what is happening as a genocide.