This is "floorsweeping", not "binning".
Floorsweeps are done when a part of a chip isn't passing tests. The defective part gets fused off and the chip gets sold as a dual core instead of a quad core, for example.
Binning is orthogonal. It's a qualitative measurement of (the part of) a chip that passes all tests. The electrical and thermal properties of a chip are tested, e.g. the leakage current and temperature are measured at different clock speeds and voltages (this is infinitely more complex for a battery powered device where voltages and currents fluctuate). The ones that pass with best results are sold as a premium product and the rest are clocked down and sold for less.
So a "K" model Intel chip comes from the best bin. An i3 chip dual core is a floorswept quad core i5. (This is what I assume, I don't work for Intel and don't know the details)
But these chips may not sell in the proportion they get manufactured in, which means that some perfectly functional quad cores get fused to dual cores and sold for cheaper. If you're lucky, you're getting one of these (and un-fusing, if possible, will work).
Floorsweeping and binning are required because the tolerances of modern semiconductor manufacturing are so tight. To get the best bin to perform well, the manufacturing process is really pushed to the extreme, which means that there will be chips that have manufacturing defects as well as lower performing chips.