I see three main reasons.
The first, monetary gain. Of course, you cannot say they are actually gaining money as we speak, since they are investing millions of dollars practically everyday just by using their military force at the moment. But, if Russia could manage to create a form of stability in this region, granted that the actual Syrian government - their ally - would remain in power, then they could eventually begin to reap the rewards. Syria would perhaps become some sort of vassal state to Russia.
Second reason, Russia wants to show their military power. Even with the recent crisis in Ukraine, Russia hasn't shown much of its strength yet. Russia has recovered from a financial collapse and now they have a stronger army, but haven't been able to show it to the world in its fullest form. Now they can do it with the Syrian conflict, and I expect them to be more and more active as the months and years go by. They are doing this because, in the future, they will want to impose their will upon the international community on numerous issues.
Third reason, and, to me, the most important one; They want to show NATO's lack of influence. Keep in mind that NATO was initially created to stop Russia from expanding after WW2. The recent conflict in Crimea/Ukraine has shown an obvious decline in NATO's will to ensure peace by using its military power. Putin wants to keep digging. He wants to show how useless NATO is. By doing so, he also creates divisions within the international community. It would definitely help him if he ever wants to invade other countries such as Ukraine.