The political system that Russia operates under is called "sovereign democracy," a term coined by Vladislav Y. Surkov. Sovereign democracy is a system which "preserve[s] the electoral process but hollow[s] out institutions capable of challenging the Kremlin's power."  It is essentially a system designed to keep the Kremlin in power but channels the anger of people into the voting booth. To accomplish this end, Surkov used a mixture of the youth movement Nashi, the United Russia party, and the might of the Kremlin to help Vladmir Putin consolidate his authority over his first two terms. (The group Nashi is a pro-Kremlin youth movement that is extremely nationalistic and patriotic which may have plans to turn their membership into political candidates to run the country. )
Over his two terms, Putin consolidated and centralized power at the federal level, ejected corporate interests, and expanded the Russian economy.  This centralization of power at the federal level has come at the expense of regional governments and helps in turning Russia more and more back to the Communist era when all power was in the hands of the federal government. This concentration of power by Putin has been going on since 2000 when legislation was passed that gave "the Russian president power to replace any regional leader and disband any parliament guilty of enacting legislation 'in violation of federal law.'"  However, one could argue that centralization of power was needed as in the late '90s there was a large gain in regional autonomy which could potentially have weakened the rule of law and had negative implications of Russian state integration. 
The current protests are taking place due to election fraud which kept Putin's United Russia party in power of the Duma, although with a smaller majority. There are a total of seven political parties in Russia, though the most powerful party is Putin's United Russia. United Russia's main goal for the country is to keep power in the hands of the Kremlin and is extremely nationalistic and emphasizes law and order. While they have political allies such as the Right Cause party, there are still exists a major opposition to the Kremlin in the form of bloggers, banned political parties, and environmentalists. Essentially, the political battle in Russia is between the old guard who wants to uphold Soviet style authoritarianism and liberals.
However, in this battle, outside forces are currently at play. Putin has been reported as stating his refusal to negotiate with protesters and has accused the US of backing the protests. While it may seem as if Putin is trying to blame the protests on America, this accusation may have some merit.The National Endowment for Democracy (NED) is backing several NGOs and political groups in Russia.  This is reminiscent of the US backing civil societies in Egypt and then having them spring to action when the Egyptian revolution came about. It also may remind one of the current situation in Syria where the US is backing the moderate Islamic civil society group Movement for Justice and Democracy.
In addition to this, the new US ambassador to Russia, Michael McFaul, is on the board of directors for both the NED and Freedom House.  Thus, there is a case to be made for US-meddling in the Russian protests elections. The US has had problems with Russia, especially over NATO expansion and the American missile defense system. Tensions have also been ratcheting around the Iranian nuclear program and the ongoing situation in Syria.
It seems that the protest movement, which must like the Arab Spring is a legitimate desire of the people for radical governmental reform and change, may be co-opted by the United States and made to serve US interests. Thus, the people of Russia must remain vigilant of outside forces while at the same time ensuring that their voices are heard and demands met.
1: http://www.nytimes.com/2011/12/28/world/europe/putin-takes-another-swipe-at-russian-protesters.html2: http://news.bbc.co.uk/2/hi/europe/4491633.stm3: http://english.peopledaily.com.cn/90001/90777/6365190.html4: http://www.wnd.com/?pageId=74545: http://www.gwu.edu/~ieresgwu/assets/docs/ponars/pm_0039.pdf6: http://www.ned.org/where-we-work/eurasia/russia