Biological Filters
The main function of a biological filter is not to remove debris, or even algae from the koi pond, but to convert pollutants such as ammonia from fish wastes and decaying matter such as leaves and uneaten fish food into relatively harmless substances.  These substances are converted into nitrates by the biological filter which can be absorbed by plants as a nutrient.  Of course, an excess of nitrates will cause more algae in your Koi fish pond.  To avoid this problem be sure to have a sufficient number of oxygenating plants in your pond.  The work well in absorbing nitrates.  You can purchase oxygenating plants at:
LiveAquaria.com: The Trusted Source for Pond Plants.
A biological filter will contain two or more layers of medium such as gravel that harbor large amounts of beneficial nitrifying bacteria that are found naturally in ponds.  As the pond water slowly flows through the medium contained in the biological filter, these bacteria break down the toxics such as ammonia as well as the nitrites which result from the breakdown of ammonia, into nitrates.  A more complex biological filter may incorporate mechanical prefilters, or have compartments that are filled with an activated charcoal  zeolites or other media.                                                                                                                             

An aeration tower will provide additional oxygen for beneficial bacteria.  When purchasing a biological filter, look for one that has this feature.   In the aeration tower, dirty water is pumped from the koi pond through the tower to the bottom of the filter.  Here it slowly moves up through the medium of your biological filter.  This gives the bacteria a chance to eat its fill.  It exits near the top of the filter and through a return hose or pipe back to the koi pond.  You can hook the return hose through a waterfall if you like.

Cleaning a biological filter is not difficult.  About once a month, drain the filter by opening a drain valve to remove accumulated silt and sediment.  This can be used to fertilize garden beds.  Afterwards, lightly rinse the filter medium to remove trapped debris.  Be sure not to rinse with a heavy spray of chlorinated water as this will likely dislodge or even kill the beneficial bacteria that reside in your filter's medium.  At the end of the season you can give your biological filter a more thorough cleaning  as bacteria won't survive below 55 degree temperatures.

Biological filters do not require a high flow rate to operate efficiently.  The pump needs to turn iconicon over the total koi pond's volume over once every four to six hours.  Initially, even though they are more expensive than the mechanical filter, they use less electricity.  Biological filters need to be run all the time and will not start working efficiently until several weeks after they are installed.  You can give them a dose of "starter" bacteria.