What gives a monitor it's resolution?

Pixels are not "put on the television". Resolution refers to the # of pixels in a given area. A pixel's, or picture element's density on the screen is responsible for what we call resolution. Smaller pixels mean better resolution because more of them exist is a given area.

RGB and displays

One common application of the RGB color model is the display of colors on a cathode ray tube (CRT), liquid crystal display (LCD), plasma display, or LED display such as a television, a computer’s monitor, or a large scale screen. Each pixel on the screen is built by driving three small and very close but still separated RGB light sources. At common viewing distance, the separate sources are indistinguishable, which tricks the eye to see a given solid color. All the pixels together arranged in the rectangular screen surface conforms the color image.

By using an appropriate combination of red, green, and blue intensities, many colors can be displayed. Current typical display adapters use up to 24-bits of information for each pixel: 8-bit per component multiplied by three components (see the Digital representations section below). With this system, 16,777,216 (2563 or 224) discrete combinations of R, G and B values are allowed, providing thousands of different (though not necessarily distinguishable) hue, saturation, and lightness shades.

One use of the term “display resolution” applies to fixed-pixel-array displays such as plasma display panels (PDPs), liquid crystal displays (LCDs), Digital Light Processing (DLP) projectors, or similar technologies, and is simply the physical number of columns and rows of pixels creating the display (e.g., 1920×1200). A consequence of having a fixed grid display is that, for multi-format video inputs, all displays need a "scaling engine" (a digital video processor that includes a memory array) to match the incoming picture format to the display.

Note that the use of the word resolution here is a misnomer, though common. The term “display resolution” is usually used to mean pixel dimensions, the number of pixels in each dimension (e.g., 1920×1200), which does not tell anything about the resolution of the display on which the image is actually formed: resolution properly refers to the pixel density, the number of pixels per unit distance or area, not total number of pixels.

For example, a 15 inch (38 cm) display, whose dimensions work out to 12 inches (30.48 cm) wide by 9 inches (22.86 cm) high, capable of a maximum 1024×768 (or XGA) pixel resolution can display around 85 PPI in both the horizontal and vertical directions.

This figure is determined by dividing width (or height) of the display area in pixels, by width (or height) of the display area in inches. It is possible for a display’s horizontal and vertical PPI measurements to be different (e.g. a typical 4:3 ratio CRT monitor showing a 1280×1024 mode computer display at maximum size, which is a 5:4 ratio, not quite the same as 4:3). The apparent PPI of a monitor depends upon the screen resolution (that is, number of pixels) and the size of the screen in use; a monitor in 800×600 mode has a lower PPI than the same monitor at 1024×768 or 1280×960 mode.

In June 2010, Apple Inc. announced and launched the iPhone 4, with its “Retina” LCD boasting 326 PPI (960×640, 3½″ diagonal, each pixel only 78 μm).[3] [4]

In January 2008, Kopin Corp. announced a 0.44″ (1.12 cm) SVGA LCD with an astonishing pixel density of 2272 PPI (each pixel only 11¼ μm).[5][6] According to the manufacturer, the LCD was designed to be optically magnified to yield a vivid image and therefore expected to find use in high-resolution eye-wear devices.

For example in moderd computers graphics cards raster imagery as set frames per second, if the resolution on the screen is set to high the graphics card will not be able to process the data, or fill all the pixels fast enough thus fail.

http://en.wikipedia.org/wiki/Display_adapter

So to finaly answer your question this is what the set resolution is on a screen.

3-bit RGB

8-bit RBG

16-bit RBG

24-bit RBG

30-bit RBG

32-biy RBG

48-bit RBG

In 30-bit Integer RGB color representation, colors are stored in three 10-bits channels, resulting in 30 bits of color data per pixel. This representation may be employed to store 210 or 1024 different values per channel, which enables the storage of 230 or 1,073,741,824 (approximately one billion) distinct colors.[25]

In 48-bit Integer RGB color representation, high-precision colors are stored in three 16-bit channels, resulting in 48 bits of color data per pixel. This makes it possible to represent 65,536 tones of each color component instead of 256, hence resulting a total or 248 or 281,474,976,710,656 (approximately 281 trillion) colors.[26]