Bits refer to digital word length which describes a signal at any moment in time. The higher the bit depth, the exponentially higher points there are available in the word length. In audio, 24-bit is the standard for recording as it provides greater dynamic detail and headroom to avoid clipping. However, before being placed a CD, recordings must be converted to 16-bit format.
Dithering is an essential process when converting from a higher bit depth to a lower one. The process makes digital truncation errors less noticeable to the human ear by introducing low-level noise which effectively masks this distortion. In addition, you may often choose the noise shaping profile of the dither to emphasize different frequencies. The effects of dither are not always immediately noticeable.
Actual conversion is a simple process which can be accomplished in any digital audio workstation or wave editor. To convert the 24-bit file to 16-bit, simply add a dither plug-in as the last effect on your master track and bounce or render the audio to a new file with 16-bit format selected.