Early on in the campaign when she was way ahead of other candidates, "sense of entitlement" was used to criticize her for being the establishment candidate; it was used to imply that she was supported by the backroom boys and was propelled into the lead by her connections and position. As the campaign unfolded, this characterization was shown to be utter fiction - not just because she does not have the backroom boys sewed up, but also because everyone has had to admit that she's an enormously hard working, scrappy politician who keeps trying her hardest day in and day out, even in the face of terrible setbacks.
Now that she's losing, Hillary's critics are twisting the sense of entitlement barb to characterize her as some sort of latter-day Marie Antoinette - a vain aristocratic bitch who feels the party owes her the nomination and so will not back down from the race, even if it means destroying the party's chances in November. But the reality is that it's a tight race and it isn't over. Democratic primaries are won when one candidate gets a majority of delegates, and neither candidate has enough support for that. Hillary's popularity took a nose dive during a key part of the primary season, but her recent 10-point margin of victory in Pennsylvania indicates that Hillary has her momentum back. Hillary has a strong case to take to the superdelegates, given her uncounted victories in Florida and Michigan, her margin of victory in electoral college votes, her success in strategic states, and her wins in every big state except Illinois. It's not a slam dunk for Hillary by any means, but it's not over.
Hillary's public record shows a person who has never had a sense of entitlement. As first lady she didn't bask in the glow of her husband's success; she was the most active presidential spouse in history. She took on major policy initiatives, took risks, got pummelled sometimes. When she became a US senator Hillary was widely praised for her hard work, for listening to all sides, and for sticking to her junior status when she could have used her fame to grab the limelight.
Serious contenders for US president are, by definition, supremely ambitious, political and confident. They have to appear ready to take on the most powerful job in the world. In campaign speeches they always say "when I am president" not "if I am president." In this sense they all have a "sense of entitlement".
But in its use as a condemnation of Hillary, "sense of entitlement" has other connotations: that she is haughty, arrogant, the sort of person who makes other people do her dirty work. It's a code word for "rich bitch." It's also a way of saying that she has stepped out of her place - that as a woman she does not deserve to feel entitled to run for president. It's just another in a long long list of sexist criticisms that have undermined Hillary as a serious candidate for president.