Dither is used when you need to reduce the number of bits. The best example, and one that is commonly used, is when dithering down from 24 bits to 16 bits or 16 bits down to 8 etc...Most commonly, dithering from a higher bit depth to a lower one takes place when a project you are working on needs to be bounced down from 24 bits to 16 bits using dithering algorithms.
So, what is the process; in mortal language of course?
A very basic explanation is we add random noise to the waveform when we dither, to remove noise. When we truncate the bits, ie in this case we cut down the least significant bits, and the fact that we are always left with the stepped like waveforms in the digital process, by adding noise we create a more evenly flowing waveform instead of the stepped like waveform. It sounds crazy, but the noise we add results in the dithered waveform having a lower noise floor. This waveform, with the noise, is then filtered at the output stage. I could go into this in a much deeper context using graphs and diagrams and talking about probability density functions (PDF) and resultant square waves and bias of quantisation towards one bit over another. But if I did that you'd probably hate me. All that matters is that dither is used when lowering the bit depth and that this is an algorithmic process, ie using a pre determined set of mathematical formulae.
If we take the 24 bit project scenario and select to bounce the resultant audio without dithering then the last eight bits (also know as Least Significant Bits) of every 24-bit sample are discarded. In terms of audio integrity you will not only lose resolution but also introduce Quantisation Noise. Because dithering adds random noise to the lower eight bits of the 24 bit signal whilst maintaining stereo separation the quantisation noise is dramatically reduced. It then makes sense to dither from 24 bits to 16 bits rather than bounce without it.
How well the process is executed is down to how good the dithering algorithms are. But to be honest these algorithms are so good nowadays that even standard audio sequencing suites (Cubase, Logic etc) will perform dithering tasks without much problem.
My recommendation is to always work in 24 bit and dither down to 16 bit for the resultant file, as CD format is still 16 bits.