When referring to computer processors, quad-core is a technology that enables four complete processing units (cores) to run in parallel on a single chip. Having this many cores give the user virtually four times as much power in a single chip. For the computer to take full advantage of quad-core, it must be running on an operating system that supports TLP and for applications to support TLP.
The number of threads that a quad-core processor has available to process requests differs by processor. To determine how many threads a particular quad-core processor can handle, check the manufacturer's website for the specifications of the processor.
You can essentially think of quad-core as a computer that has four central processing units.