At the end of September 2015, Russia began airstrikes in Syria in support of its ally, controversial Syrian leader, Bashar al-Assad. Why?

Russia has a naval installation in the Syrian port of Tartus providing Russia with strategic access to the Mediterranean Sea.
Syria buys billions of dollars worth of defensive weapons from Russia.
Russia doesn't believe that the United Nations or any other group of countries have the right to change Syria's regime. (If this can happen in Syria, Putin worries, then he could be targeted just like Libya's leader, Muammar Gaddafi, in 2011).
Russia is trying to assert itself as a leader in international affairs both to prove to the world that the country is strong and to instill pride and patriotism internally.
Putin wants to direct attention away from the conflict in Ukraine (Russia faces international economic sanctions because of its 2014-15 invasion and interference in the former Soviet Republic of Ukraine).

Why does this matter?

Russia, as one of five permanent voting members of the United Nations Security Council (along with the U.S., U.K., France, and China) can veto any resolutions drawn up against Syria (resolutions can only pass with unanimous approval).