If your input resolution is lower than your display resolution, the video must be processed to “fill in” the extra pixels. Upscaling Software is the key to the process, recent more intelligent algorithms can make a big difference to the result, giving a sharper image.

The Cathode Ray Tube (CRT) made up the picture elements by scanning three beams of electrons through a mask of roughly one million holes, to land on red, green or blue phosphors.
The old technology was ok up to 32 inch displays, but had production problems in size and costs above that size. Also the displays became inaccurate at the edges causing colour fringing and poor focus.
In addition overscanning and incorrect adjustment of width and height often meant viewers didnt have the full picture. Scanning was always done at 625 Lines, interlaced, irrespective of the inputs actual digital resolution.
Digital Display Technology: Plasma, LCD, LED and DLP Projectors

When digital tvs entered the market they differed in one important respect to the older tube type tvs; they had a fixed resolution ie. they had a fixed number of pixels ( smallest possible part of a picture display ) , this is usually given as the tvs native resolution.
Illumination of the pixel is controlled by sending signals to a combination of column and row, addressing just one pixel. The Native Resolution then of the tv is determined by the number of rows and columns, typical TVs are
- 480 = 720 columns and 480 rows (SD)
- 720 = 1280 columns and 720 rows (HD “ready”)
- 1080 = 1920 columns and 1080 rows(HD)
The letters i or p always follow the resolution figure. The digital display is progressive ( p ) , the i indicates ‘interlace’ . Older tube tvs used this clever technique called interlacing or sending the odd numbers lines, then interlacing them with the even numbered lines, this cut down the rate at which the frames were sent out by half, the persistance of vision and decay of illumination of the phosphors ensured the previous lines were visible just long enough to stop flicker. Digital displays can easily switch from i interlaced to p progressive scanning.
Interpolation
So what happens if your tv is 720p resolution, but the incoming signal is 480i? or any other combination? The final picture displayed must be interpolated to fit the native resolution. A mathematical process is applied to the incoming signal so it is displayed properly. Not so easy with the older tube type tv, high power electronic switching was used to change the scanning width and or height; but with digital displays the solution is much better.
Extra bits are introduced to fill up the available pixels, or taken away if the display resolution is lower than the signal resolution. Digital electronics is perfect for this process, mathematical algorithms can change the incoming signal to match the tv display in microseconds. Many other computer peripherals also use interpolation, printers and scanners for example.

As an example, consider the processing which must take place to convert an input image in 4:3 format 720X480 resolution from a DVD, to display on a fixed pixel display unit 16:9 format 1920X1080 pixels. There are about 6 times as many pixels to fill, as there are coming from the input. To achieve this digital FIR filters are used. These are mathematical algorithms. The design of these is critical to the quality of the output. As time has progressed, circuitry has become much better at doing this, more complex of course, but better too at dealing with some of the side effects of upscaling, like jagged edges, motion adaptive noise reduction and mosquito noise.