Power and influence

Warren is not running for President. But she is mounting a campaign to insure that Clinton and other prominent Democrats adhere to her agenda of reversing income inequality and beating back the influence of corporate power in politics. These are issues that Warren has pursued for three decades, as an academic, a policy adviser to Democrats, an Obama Administration regulator, and, since 2012, a U.S. senator and the anchor of a progressive wing of the Democratic Party.
[...]
One of Warren’s advisers believes that if she entered the race against Clinton she would be shredded by the Clinton political machine. Instead, the best way to pursue her agenda is to use the next year to pressure Clinton.
“I think she’s in a beautiful position right now,” the Warren adviser said, “because she can get Hillary to do whatever the hell she wants. Now the question is, will Hillary stick to it if she gets in? But at the moment Elizabeth can get her on record and hold her feet to the fire.” 

The New Yorker: The Virtual Candidate, April 2015

The Atlantic argues that Clinton is not "ideologically one-dimensional" as Warren is (who is defined by her economic views), but

If Hillary’s advisors are angry that the press doesn’t describe her as “left-wing” anymore, they themselves are partly to blame. That’s because they, and she, have spent much of the last two decades trying to overcome exactly that reputation.  

The Atlantic: The Many Measures of Hillary Clinton, April 23, 2015

And here's a piece on Hillary Clinton's views on the Trans-Pacific Partnership. 

The problem for Clinton is that she has historically backed free-trade deals, and as secretary of state called the TPP "the gold standard in trade agreements." Yet her campaign's big push over the last week or two has been to prove her liberal bona fides. Many progressives still don't like NAFTA, a product of Bill Clinton's administration (actually, many Americans don't like NAFTA), and while Hillary Clinton still looks like a prohibitive favorite in the Democratic primary, rivals like O'Malley and Senator Bernie Sanders oppose it, as do the labor unions that are a major part of the Democratic coalition. 

The Atlantic: Hillary Clinton's Hard Choice on Free Trade, April 23, 2015

Bernie Sanders is expected to announce his intent to run for President next week, and even though he is an independent Senator (from Vermont), he will seek the Democratic nomination. Warren seems to have no intention to run and Sanders is very unlikely to win the nomination, but regardless, their presence in the conversation will have a severe effect on how Hillary Clinton will have to conduct her campaign, and where she positions herself on issues important to the liberals within the Democratic party (which is an interesting thing to keep in mind when it comes to winning contested states, perhaps also having to appeal to swing voters, but also within the context of a severely polarised political landscape).