The four big reasons that Russia wants to protect Assad, the importance of which vary depending on who you ask, are: (1) Russia has a naval installation in Syria, which is strategically important and Russia's last foreign military base outside of the former Soviet Union; (2) Russia still has a bit of a Cold War mentality, as well as a touch of national insecurity, which makes it care very much about maintaining one of its last military alliances; (3) Russia also hates the idea of "international intervention" against countries like Syria because it sees this as Cold War-style Western imperialism and ultimately a threat to Russia; (4) Syria buys a lot of Russian military exports and Russia needs the money.
Iran's thinking in supporting Assad is more straightforward. It perceives Israel and the United States as existential threats and uses Syria to protect itself, shipping arms through Syria to the Lebanon-based militant group Hezbollah and the Gaza-based militant group Hamas. Iran is already feeling isolated and insecure; it worries that if Assad falls it will lose a major ally and be cut off from its militant proxies, leaving it very vulnerable. So far, it looks like Iran is actually coming out ahead: Assad is even more reliant on Tehran than he was before the war started.
5. This is all feeling really bleak and hopeless. Can we take a music break?
Oh man, it gets so much worse. But, yeah, let's listen to some music from Syria. It's really good! [http://wapo.st/1934Lfk]
If you want to go old-school you should listen to the man, the legend, the great Omar Souleyman (playing Brooklyn this Saturday!). Or, if you really want to get your revolutionary on, listen to the infectious 2011 anti-Assad anthem "Come on Bashar leave." The singer, a cement mixer who made Rage Against the Machine look like Enya, was killed for performing it in Hama. But let's listen to something non-war and bit more contemporary, the soulful and foot-tappable George Wassouf.