The tragic death of the Russian ambassador in Turkey is indirectly related to Syria. The attacker stated that "We die in Aleppo, you die here". It seems the that attacker's motivation was to retaliate for the Russian support of the Assad regime. The Russian support for the Assad regime is a cause of concern for many countries. The Turkish support for the rebels only increases the tension between Russia and other nations.
Russia has taken a significantly greater role in the Syrian civil war than most nations, the United States included. As a result, dissidents who oppose Russian involvement (or criticize the level of involvement) are likely to emerge from the "woodwork." Russia has engaged in extensive bombing campaigns in Syria. This likely played a role in the shooting.
Obviously, the gunman was very upset about the situation in Syria, and rightfully or wrongfully, he blamed Russia and this ambassador for it. This person went on a rant after the shooting that we all saw. He said that the attack was because of Russia's stance on the war in Syria. He had a dark motive and did a terrible thing.
The gunman mentioned Syria both in Turkish and in Arabic at the time of the attack. It seems to be somehow related to Turkey's frustrations with Russian involvement in the killings and all of the destruction in Syria. It's not clear if gunman was acting on behalf of a particular organization, but it's pretty safe to say it's related to Syria.