If the tubes are biased so they receive too much current, they can begin to interfere with each other and cause crossover distortion. While you may sometimes want to add a distortion effect, it is better to do so with a pedal so you have the option of using the amplifier to produce a clean sound.
Reducing the current allows both tubes to operate simultaneously. While this produces a cleaner sound, it also causes the tubes to generate more heat, which can be detrimental to the life of the tubes. Reducing the current also reduces the overall power of your amplifier. If, in an effort to produce a cleaner sound, you reduce the bias beyond a certain threshold, the amplifier will become nearly inaudible.
The goal of re-biasing after changing tubes is to find the right level of current that balances heat generation and power with distortion. Because all tubes have different capacities for conduction, you will have to re-bias each time you install new tubes to make sure the tubes are achieving the proper balance.