Two huge and powerful nations, Russia and the US, do have interest in what happens in Sytia. Part of this is pride: they have each invested hugely in military involvement. It would be tremenedously to their credit internationally if they could legitimately claim their intervention brought the war to an end. This would be difficult because of the number of factions within Syria and the number of countries outside that are involved.
Both Russia and the US recognise that massive destruction that would accompany a direct conflict. The other aspect is access to Syria's natural resources. Both countries have interest in the oil-rich region the US controls in northern and eastern Syria. Russia supports President Bashar al-Assad who plans to seize the wheat and oil fields.
Syria is considered to be Russia's ally in the middle east. Russia has stood by Syria during challenging circumstances and forming coalitions is necessary for meeting shared goals. Russia wants to fight the dispute in Syria on its terms, which conflict with the intentions of the US.
The United States wants Assad out of power so that the oil pipelines are fair game. Obama set forth that we have a moral obligation to intervene. Also, the United States was founded on the belief that people should govern themselves. The US cannot just abandon a region that is fighting for their rights.