"I'm not fat ... I'm big-boned!"
-- Eric Cartman in South Park
"Big-boned" has become a euphemism for being overweight or obese, but really it means what you'd think it means: a person who has a sturdy, wide skeleton. Think of Gimli rather than Legolas, Samwise rather than Frodo
A bigger frame means a heavier frame. It also means one can comfortably carry around quite a bit more extra weight -- be it muscle or fat -- than a person with a smaller frame.
Take a look at the offensive line of any NFL team or the governor of California: big-boned, the lot. Now look at the willowy, waifish lads in late 90s heroin chic fashion ads. Not big-boned. Take a look at pro tennis player Venus Williams. She's tall, strong and muscular, and she's built like a whip. Now take a look at her sister Serena, who is shorter, has wider shoulders, wider hips ... bigger bones.
Even when a big-boned person hasn't got enough fat on his frame to make a decent bar of soap, he still has a square look about him (Sean Astin, even though he's dropped all his fat-hobbit weight, still looks pretty solid). The big-boned person typically has wide hips, wide shoulders, a wide face, and a broad ribcage. Big-boned people will often -- but certainly not always -- seem to have shorter arms, legs, and fingers.
The standard, oft-used-in-health-magazines test for determining whether or not you are truly big-boned adheres to the notion that large-framed folks will have proportionally shorter limbs and digits. The test involves trying to encircle the bony part of your wrist with your thumb and forefinger. If your thumb and finger don't meet -- tah dah! You've got a large frame. You're big-boned, and are consequently going to weigh more for your height than your small-boned bretheren despite your efforts at dieting and exercising.
But that test breaks down with people who don't have "standard" proportions; it's quite possible to have a barrel chest and long fingers, or ultrawide hips to go along with long legs. For examples of such anomalous body types, go to a professional symphony concert and take a look at the string bass and tuba sections (I have known small, delicate people who play these instruments, but they're less able to handle the physical stress of hauling the huge instruments around; conversely, folks with stubby fingers tend not to make it as musicians).