Dither is random or semi-random noise added to a signal in order to mask quantization noise and/or extend dynamic range. The simplest dither is quiet white noise, but more complicated forms of dither are possible using noise shaping, and they can even be completely inaudible.
Bit depth reduction
A common use for dither is to improve the perceived audio quality when converting a digital signal from a higher bit depth to a lower one, e.g. from 24-bit to 16-bit. By dithering the signal with a small amount of added noise, the additional rounding error added from requantization can be decorreated from the signal, resulting in a noise floor that is mathematically slightly higher, but audibly less noticeable. The addition of dither becomes more important as the number of quantization levels decreases, and so is particularly important when converting to 8 bit or lower audio.
Is dither really necessary?
Going from 24-bit to 16-bit, the quantization error is very small and the distortion/noise is extremely unlikely to be heard in any real music. Since quantization error isn’t audible in any real music at useable listening levels, whether dither must be used is more a matter of doctrine than functionality.
Many sources (e.g. cassettes and LPs) already have considerable noise such as tape hiss. Even the best live recordings get some noise from the equipment, especially microphone preamplifiers. This might not make the best dither, but it acts in the same way, to largely de-correlate the quantization error from the signal.
Anyone who believes dither is always necessary for conversions to 16-bit should submit, on the HydrogenAudio forums, samples that can be discriminated in blind testing.