Within the chip, each core operates in conjunction with other circuits such as cache, memory management, and input/output (I/O) ports. The individual cores in a quad-core processor can run multiple instructions at the same time, increasing the overall speed for programs compatible with parallel processing. Manufacturers typically integrate the cores onto a single semiconductor wafer, or onto multiple semiconductor wafers within a single IC (integrated circuit) package.
Although it's tempting to suppose that a quad-core processor would operate twice as fast as a dual-core processor and four times as fast as a single-core processor, things don't work out that simply. Results vary depending on the habits of the computer user, the nature of the programs being run, and the compatibility of the processor with other hardware in the system as a whole.
See a brief introduction to multi-core processor architecture: