What is the role of political parties in policy formulation?

Political parties exist for the purpose of promoting the shared policy positions of their candidates and voting constituencies. When we talk about conservative vs. liberal policies, we are, in a very general way, talking about how the government should pursue its goals. Liberals generally believe that the government should intervene to help solve society's problems, while conservatives prefer to let the free market increase economic opportunity, which, theoretically, helps improve peoples' lives through their own efforts.

In order for the parties to actually put their policy objectives into practice, they have to gain enough political power, usually by gaining electoral office in Congress and/or the White House. Health care is a good example of how this works. When Barack Obama took office in 2008, one of his main goals was to establish a national health care plan. This was a goal of the Democratic Party, and had been for a long while, but they had not yet gathered the political power to put it into place. There was a major effort to do so in the 90's during the Clinton administration, but the Democrats did not have enough seats in Congress to push it through. Just because a party has a policy doesn't mean it will actually be put into action, even when the president wants it. When Obama took office there were enough congressmen supporting this liberal policy to get it passed, but just barely. 

Very soon we will be seeing a good example of how party policy is formulated and publicly presented when the Democrats and Republicans hold their party conventions to officially nominate their presidential candidates. These will be the policy positions that Clinton and Trump run on as the election approaches. The losing party is not going to have much luck putting their policies into force; even the winning party will face obstacles in Congress if they do not have clear majorities in the House and Senate.

The major parties also use policy statements to drum up support from their party members and prospective voters. They know that they are not going to be able implement everything they want, but to keep their voters interested and active, they must give voice to their concerns and give them something to hope for.

In the end, as always in politics, it will be about power. If one party can win enough seats in Congress and also win the presidential election, they will be able to enact their policy proposals. This hasn't happened often in recent years, so we haven't seen a lot of major legislation passed, with the obvious exception of the health care bill.