Cores are semiconductor designs that are meant to be used inside ASICs and FPGAs. They're also referred to as IP cores ("IP" meaning "intellectual property") or silicon IP. The chip industry prefers the latter phrase, but Light Reading tends to avoid it because the acronym "SIP" is already taken in telecom.
Entire companies are built up around creating IP cores. Many of them are small shops, less than 10 people who contract themselves out. But IP cores can be a big business too, with ARM Ltd. (Nasdaq: ARMHY; London: ARM) and Rambus Inc. (Nasdaq: RMBS) being prime examples. The key is that they deliver the design but don't build the chip themselves.
Note that a core doesn't have to be small. It can be an entire microprocessor, as in the case of multicore processors, which put multiple microprocessors onto one chip.