There are several reasons - Obama was younger, male, turned being black into an advantage in a year that was long coming post-Jesse (and how private school upbringing/white grandparents took him out of the hood think)

Obama handled social media well (Howard Dean wasn't bad but crashed) - and he was good at being enigmatic and Rorschach-like - everyone saw what they wanted.  The opposition failed to damage him, but got better at social media after 2008 and the crash/rise of Tea Party emboldened them, as did 2 years obstructing healthcare and 6 more trying to repeal, shutting down gov, stealing Obama's SC pick, etc. 

Hillary was "most admired woman" like 2 years before she was "unlikable", with various Benghazi hearings, et al along the way. Much of the damage was from far left types (wrapping Iraq around her neck, not Kerry's or Biden's, reversing chronology to make her Gaddafi comment seem more callous while ignoring Gaddafi's threats to wipe out Benghazi and making it her baby more than Obama's...). And the Roger Stone types for the Seth Rich and Pedophile pizza smears. In 2008 Obama's problem was to deflect how well Hillary was doing in West Virginia. 8 years later she was to blame, and Trump was the savior. It didn't help that Obama was overly cautious in a lot of places, so revitalizing the Appalachians didn't happen, and any Dems (i.e. Hillary) caught the fallout. The Obama bailout was tax-cut friendly, shy on payments to individuals, and he was slow stopping banks from their robo-foreclosures, so again, a lot of bitterness during the slow recovery, while blacks received much less attention due to Obama rightly-or-wrongly not wanting to appear pandering.

Yes, Hillary had her balls in a víse - any outing to talk ideas and policy and promote grrl power was met by media antipathy, pivot to her emails, etc. Easier to be likable to pre-primed adoring fans, which for females seemed attractive for a NY sec til "I don't vote my vagina" took hold from Susan Sarandon to Killer Mike. (oh yeah, wokedom started, so being white female was overtaken by PoC female, partly LGBTQ. Worth remembering that Kerry 2004 largely lost due to the shock of gay marriage (and Ohio voting machines) while 12 years later gay marriage was assured and we were on to pronouns - these are quick shifts that are hard to slalom.

Beyond that, Hillary got 3 million more votes than her opponent. Whether she ran a bad campaign for actual electoral votes or they were stolen, her performance was not embarrassing like Mondale or Dukakis. She won the popular vote, and possibly won those 3 critical Midwest swing states, barely losing the electoral vote in any case. She held her own. She made mistakes , but she ran a pretty fucking respectable campaign considering the combination of winds against her, and the kamikaze campaign of Bernie Sanders was one of them, illegal Mercers & Cambridge Analytica support for Trump another, documented hacking of DNC and Podesta by Russia's GRU a third. Yet she got 3 million more votes. Not just sour grapes - she fought hard against worst odds if you actually calculate (thank Nate Silver for that). How many US candidates could ask Russia for help on national TV and thrive? Biden just had to sit out COVID and wait for Clayburne to make him a deal after it looked like he lost. We should all be so lucky in being uninspiring. Bidens a much better president than candidate.

PS - prolly something to say about the expansion/growing influence of Fox/Sinclair, FEC going AWOL while Egypt, UAE et al made illegal presidential campaign (Trump) payments, and other shifts. Seriously, there's not just 1 issue on what campaigns succeed. You saw the video on Iowa - part includes how the Dem party runs its apparatus - in Hillary's year she had to bail them out (partly Obama's depowering them), part just the combined talent across the board, etc. In 2018 ppl (women especially) were pissed and ran a stronger campaign. 2016 there was too little urgency to combat Trump gullibility. 

SHE WAS NOT A GREAT PRESIDENTIAL CANDIDATE, GAVE OFF AN ELITIST, HOLIER THAN THOU AIR. (Most Senators do that, BTW, and that's the reason for the old adviso that they aren't good presidential candidates, and which also made her a great Senator and Secretary of State.

This is one of the dumbest things you've latched onto. Biden was a Senator candidate, Obama was a Senator candidate, JFK was a Senator candidate, Truman was a Senator aside from 3 months as VP. LBJ was Senator aside from 2 1/2 years as VP. Gore was a Senator then 8 yr VP who got a much greater % of votes than Bill Clinton either time. John Kerry was a Senator candidate who won half the vote (48.3%/251 electoral votes, just shy of Gore). Nixon was Senator after 8 years VP. Bernie Sanders was a Senator who electrified the 2016 primaries, as did Sen. Eugene McCarthy and Sen. Robert Kennedy in 1968 before former Sen/1-term VP Hubert Humphrey won the nomination. (I'll give you Bob Dole and Walter Mondale). How did so many Senators learn how to run, and how did so many VP-turned-Presidents overcome the disability of being Senator?