Things that are longed-for are wanted desperately by someone. When you finally get your longed-for job as the mascot for your city's minor league baseball team, you may cheer and jump up and down.
Many people who tried for years to have a baby describe their eventual children as longed-for, and your chocolate loving sister might even describe the longed-for double chocolate birthday cake she's been dreaming of since last year's birthday. Anything you yearn for or desire strongly is longed-for, from the "have a strong wish or desire for" meaning of long.