Capacitors act as batteries, more or less. The ones in the power supply (the rectifier board) are storing energy so that when the amp requires more current (a loud transient, for instance) than usual, the extra energy is there in the caps to cover it. It's like having a resevoir of extra energy in the power supply. When the requirements of the amp exceed the ability of the caps to provide energy, the voltages in the amp drop and the amp starts to compress. This is often called "sag" by guitarists who use tube amps. Larger caps have a larger capacity to store this energy so they provide you with more clean headroom and tighter bass (since bass requires the most energy to reproduce).
That was a VERY simplified explanation, but it should give you the basic idea.
The caps in the bias supply serve another purpose altogether. They provide stored energy as well, but the function of them is to keep the bias voltage stable so the tubes behave consistently. Larger caps in that part of the amp will keep the bias stable and also help to provide clean headroom, but they take a little longer to charge so the amp will take a little longer to stabilize. It's a good idea to let the amp warm up for a full minute or two before playing anyway, but even more so if you increase the size of the bias caps.
Enjoy your amp!
"People don't realize it, but the bass player holds the whole thing up like Atlas." -Some wino who talked to me on the subway on my way to a gig