Dithering is the intentional application of "noise" (random data) that reduces errors when converting analog data to digital data.  The conversion to digital data uses a technique to either round or truncate estimations in data

From Wikipedia:

Dither most often surfaces in the fields of digital audio and video,
where it is applied to rate conversions and (usually optionally) to
bit-depth transitions; it is utilized in many different fields where
digital processing and analysis is used — especially waveform analysis.
These uses include systems using digital signal processing, such as digital audio, digital video, digital photography, seismology, RADAR, weather forecasting systems and many more.

For Audio:
In an analog system, the signal is continuous, but in a PCM digital system, the amplitude of the signal out of the digital system is limited to one of a set of fixed values or numbers. This process is called quantization. Each coded value is a discrete step... if a signal is quantized without using dither, there will be quantization distortion related to the original input signal... In order to prevent this, the signal is "dithered", a process that mathematically removes the harmonics or other highly undesirable distortions entirely, and that replaces it with a constant, fixed noise level

In Video and Photography:

Dithering is a technique used in computer graphics to create the illusion of color depth in images with a limited color palette (color quantization). In a dithered image, colors not available in the palette are approximated by a diffusion of colored pixels from within the available palette. The human eye perceives the diffusion as a mixture of the colors within it (see color vision). Dithering is analogous to the halftone technique used in printing.
Dithered images, particularly those with relatively few colors, can
often be distinguished by a characteristic graininess, or speckled
appearance.

"Dithering is a technique used in computer graphics to create the illusion of color depth in images with a limited color palette (color quantization). In a dithered image, colors not available in the palette are approximated by a diffusion of colored pixels from within the available palette. The human eye perceives the diffusion as a mixture of the colors within it (see color vision). Dithering is analogous to the halftone technique used in printing. Dithered images, particularly those with relatively few colors, can often be distinguished by a characteristic graininess, or speckled appearance."

In web design: When a specified colour isn't available, it is replaced with the closest available colour.

If you use 32 bit colour on a web page, but the visitor only has a video card or display configured to display 16 bit colour, some of the colours you use will be replaced.