Graphics processing unit
A graphics processing unit (GPU) in a computer is an independent specialized graphics coprocessor. It is responsible for handling the graphics output of the computer, generally to the monitor. GPUs usually handle one or two outputs, often in forms like VGA or DVI. In some computers, GPUs can also handle other functions, such as video decoding. A graphics processing unit is a part of all personal computers, most workstations, and some servers. A graphics unit can be dedicated or integrated. Generally, lower-end PCs or smaller PCs tend to have integrated graphics solutions, while midrange or high-end PCs have dedicated graphics solutions on video cards.
Computers use a graphics API and driver to interact with the GPU. Drivers are generally supplied by the motherboard or GPU manufacturer, and often only work for a specific model or set of models of GPU. A computer program (such as a game) will generally use either OpenGL or DirectX to communicate with a graphics card.
Dedicated Graphics Card
A dedicated graphics unit is normally situated on a video card, and connected to the motherboard by an expansion slot, such as PCIe or AGP, and includes dedicated RAM for the graphics coprocessor to use. Dedicated RAM offers massive amounts memory bandwidth to the GPU. Additionally, because there is less graphics RAM than system RAM, the graphics RAM can be expensive low-latency, high speed RAM.
Gaming PCs sometimes include more than one graphics card, using either SLI or Crossfire, which allow pairs of Nvidia or ATi cards to work in parallel on graphics tasks.
Integrated Solution
An integrated graphics solution sits directly on the motherboard. It borrows RAM from the rest of the system to do its work. Integrated solutions are generally slower, but use less energy and are less expensive. Integrated solutions are slower both because they borrow lower-bandwidth system memory and because they tend to have slower processors. Some newer integrated GPUs are hybrids, using some dedicated memory and borrowing some system memory. This allows for better performance. Integrated solutions by definition are generally not expandable or replaceable, but some motherboards which use integrated graphics also have PCIe slots that allow for a graphics card to be added.
Sources
PC Magazine's definition Tomshardware.com's graphics cards for beginners series