Simply put, it is a faction war for power, everyone against everyone.
The longer answer is that following the Arab Spring revolutions in the Middle East, Syrians too went into the street to protest against their oppressive government. President Bashar al-Assad however -- heir to a decades-old totalitarian family regime -- didn't like this and ordered violent crackdown on the protests.
What followed were the bombing of civilians by their own government. Rebel groups rose up in response, supported by various western nations in various capacities, including the US, Britain and France. Russia, Iran and Iraq joined in on their own chosen sides, not to mention everyone from Turkey, Lebanon, Egypt and dozens more. While not all of these nations have boots on the ground, many are participating either financially, delivering weapons and aid, and even launching air and ground strikes.
As such it has been called a proto-World War by proxy, with the capability of escalating into something of a Third World War. This, as we can all agree, is no laughing matter. Russia, China and even North Korea for example are on opposite sides of Europe and the US, with circumstances harking back to the Cold War days.
A few of the countries involved and their allegiances.
To top things off, the Islamic State of Iraq and the Levant (ISIS or ISIL) a powerful jihadist militant group -- self-styled as a caliphate and Islamic state -- has seized the opportunity to meddle in the war and conquer large areas of the country as part of their caliphate. This has been frowned upon by everyone, and so while the US and Russia for example are backing opposing factions, they are also both bombing ISIS. The Islamic State retaliated with attacks on everyone.
Because of this it has also become a religious war, with warring Islamic factions against each other, but also Islamists against Christians.
A few of the factions and their current territories. Click to expand. (as of November 2015)
It's a veritable mess that has been going on for nearly 5 years now. As if the millions of war-displaced refugees now wandering through Europe weren't enough, the recent massacres in Paris shifted the issue more into the spotlight, highlighting the global reach of the problem. And with so many factions, parties and countries involved, each with their own reasons and agendas, this is no problem easily remedied.