Bi wiring your speakers properly can acheive improved results, this enables each unit in your speakers to be run separately, feeding each unit with a separate signal enhances the sound output quality considerably although most critics would say just upgrading the cable itself will yeild the same results.
Thing is, not many of us are doing it right, the first most common way it seems is to get some bi-wire cables terminated at each end with good quality banana plugs, the thing is one end of the cables will be terminated with 2 plugs and the other with 4, this way is questionable, you see the whole point of bi-wiring is to send a separate signal to each driver in your speaker, and the other obvious benefit it is believed your amplifier will not have to work as hard through each channel as each speaker is being powered by shared output, meaning that half the effort is needed from set Aset output and the other half of the effort is run from set Bset output of the amplifier as they are running one unit instead of both, if you use just Aset speaker output only then your amplifier will be running the same as it would weather you remove your bi-wire links in your speaker terminals or not.
Lets say you have cable with 2 banana plugs on the amplifier end and 4 plugs on the speaker end, you then plug it all together, your bi-wired right? wrong, you are using the same signal from the one amplifier output to run that speaker, you may as well leave your link plate in your speaker as you have the same signal running both terminals, that way is common used for amplifiers with just 2 speaker outputs but your gaining nothing, this way is questionable and not classed as bi-wiring and you can infact wire your system up this way and STILL put your link pins back in your terminals without any difference, kinda proves my point.
The next way is probably the best way you can bi-wire your speakers properly with the average 4 speaker output amplifier, if your amplifier has 2 sets of speaker outputs, set A and a set B then its thumbs up for you, this is as close to proper bi-wiring the average joe is gonna get, set A speaker outputs should be used to run the lower terminals on your speakers, set B speaker outputs on your amplifier should be used to run the top terminals on your speakers, this way the amplifier is sending a separate signal filtered through the amp and is less work for your amp, you are gettings different signals to your speakers, the difference is audible to good ears, time after time i have found this the best way by far, but dont forget you will need 4 banana plugs on each end of your cables, please make sure your bi-wire link plates are removed from the speaker terminals when using this method as not doing so will break your amplifier.
The hi-end bi-wiring way or called bi-amping is to use 2 or 4 power amplifiers, each amplifier will power each speaker, one amp for the tweeter and one amp for the woofer and so on and is almost never heard of anymore.
No responability is held by me should your equipment fail by the methods shown above, you need to make sure you have an amplifier with equal outputs, meaning if set A output is 8ohms then set B needs to be the same, idealy an amplifier will say 6-16ohms on all outputs, or 6-8ohms or 8-16ohms, note not all amplifiers with 2 sets of outputs are ok for this application.
Bi amping is totally different from above and is not related in any way.
Bi-Amping is simply a separate amplifier to drive each unit, a 2 way speaker requires 2 amplifiers, a 3 way 3 amplifiers and so forth.
Also consider powered crossovers or active crossovers.