After capturing at least four important states this week, Hillary Clinton has all but locked down the Democratic nomination and, barring a disastrous stumble, will face the Republican nominee in the general election in November.

So what have Democrats learned about their putative nominee after 29 contests thus far? As the battle with Vermont Sen. Bernie Sanders progressed, the former secretary of state grew stronger as a candidate, but she displayed vulnerabilities that a Republican ticket could potentially exploit.

Her debate performances strengthened, she developed a clearer message, and she revived parts of Barack Obama’s voting coalition by fully embracing the president’s record and legacy. She said recently she isn’t a natural-born politician in the mold of her husband, former President Bill Clinton—an admission that might help her seem more genuine to voters.

And after getting a scare from Mr. Sanders, her supporters said she showed resilience that will prove helpful once the general-election race begins.

“Bernie has made Hillary a much better candidate,” said Patti Solis Doyle, Mrs. Clinton’s campaign manager in the 2008 presidential race. “She has been able to fight for her candidacy, been able to stumble and make corrections. She’s been able to go at it one-on-one on the debate stage and really hone those skills again.”