Many brewers on this forum leave the fermented beer on the trub (sediment) in the "primary" for at least 3 weeks. This allows the yeast time to clean up some of the byproducts of fermentation that they produce. After this time, you can rack into a "secondary," which is really just a clearing (brightening) tank or you can rack into your bottling bucket if fermentation is complete. (There is really no need to "secondary," although many feel it produces a clearer beer.) You can verify this by taking hydrometer readings two or three days apart and if the SG is the same, fermentation is probably finished.
The trub (sediment) on the bottom of the bucket is made up of flocculated yeast, some break material, and hop residue. You should really leave it behind to obtain a clearer beer. The beer will still have millions of live yeast cells per milliliter, which will be more than enough for carbonating.