At Brookings, John Hudak, Senior Fellow for Governance Studies, explains why “If Clinton wins in November, she’ll have Sanders to thank“:

Sanders has managed something Clinton has been ill-equipped to do: connect with a variety of demographic groups who love Barack Obama but feel left behind by Obama’s recovery. Clinton has cloaked herself in the Obama record, and, in the process, she has alienated those who have not reaped the fruits of his progressive labor.
…No one expected that so many Americans would “feel the bern.” Media, the party, voters, and Brooklyn were all caught off guard by Sanders’ appeal. Yes, Sanders can be labeled a one issue candidate, or too extreme, or unelectable, but there is a reality in his message. He’s tapped into a growing discontent among liberals, moderates, and conservatives that the system is stacked against them and change was necessary. Americans are angry, and love him or hate him, Bernie Sanders has effectively talked to those angry voters. Hillary Clinton has not.
Although Bernie Sanders is less likely to be the Democratic presidential nominee now than he was even a week ago, that should not diminish his importance in this race and the impact he has had on Secretary Clinton.

Hudak adds that “He ran and continues to run a campaign of big ideas that connects with many voters…young voters, voters of color, moderates, conservatives, and anyone who feels betrayed by the current state of American politics. That is a big group that most candidates–Clinton and every Republican candidate but Trump–has underestimated.”
As the first woman candidate for president to be widely-considered a front-runner, Clinton deserves great credit for her impressive accomplishments and it would be folly for any of her adversaries to underestimate her capabilities. She has survived a couple of decades of relentless villification and emerged tougher, battle-tested and well-prepared to prevail over the most obstructionist political party in U.S. history.
But, like all candidates, Clinton has her vulnerabilities, and Hudak credits Sanders with helping her face her shortcomings as a candidate:

…He has injected passion into the Democratic race–a passion Clinton would not inspire if she marched to the convention in Philadelphia devoid of competition, readying herself for a coronation…Sanders supporters have pushed Clinton in directions she never expected to go. They have made her change her language, her message, and her campaign style. It is not the path she wanted, but it is probably the path that best serves her. Bernie Sanders has pushed her to the left on many issues, but he has also made Clinton a better candidate. And my guess is she knows it.
…He brought to the surface a variety of issues that Clinton had to address–income inequality, corporate power, campaign finance, and others–that she may have only paid lip service to but for a legitimate primary challenge. Sanders may not have changed Clinton’s mind, but he surely changed her message, and that is a good thing for any Democrat.
She has been forced to take on a series of issues that matter to Americans of all stripes, and she will enter the general election campaign stronger for it. Combine all of that with the passing of Justice Scalia and the prospect that the Senate may hold up the confirmation of his replacement, the Clinton candidacy and its prospective Supreme Court pick becomes all the more important in the grander scheme of American politics. The desire to overturn Citizens United seems almost liturgical to the Sanders campaign and must now be a central part of the thinking of a future Clinton administration…He pushed Secretary Clinton to think and talk and address a series of issues that will make her a better candidate in November. That rhetoric will ultimately help bring many Sanders supporters into her corner.

“Sanders’ insurgence may not have been the external shock Clinton wanted or expected,” adds Hudak, “but it may have been the medicine she needed.”
Hudak is not worried that Sanders supporters will not vote if Clinton is nominated. Even though Clinton may not inspire them like Sanders, “the prospect of a Trump or Cruz or Rubio candidacy will.” Further, concludes Hudak, “In 11 months, if Hillary Clinton stands on the West Front of the Capitol to swear the presidential oath, she should thank the junior senator from Vermont for part of that success.