To power an amp or preamp, the power supply converts the
AC ("alternating current") power (from the wall via the power transformer) into
DC ("direct current"). The first step in doing so is rectification, which turns the negative "phase" of the AC "upside down" into a positive one (speaking in very general and fuzzy terms).
Rectification can be done with solid state diodes, or with tube diodes. Some say they prefer the sound when tube rectifiers are used; possible reasons for this are that tube rectifiers have a higher internal impedance than solid state ones and thus cause some "sag" in the power supply which might interact in a beneficial way with some circuits, and that tube rectifiers "turn off faster" thus reducing high-frequency noise induced into the power supply.
The power is then filtered with capacitors and sometimes inductors to turn the bumpy rectified waveform into a smooth voltage that can be used to power circuits. The "bumpy" part is called "ripple." A
voltage regulator can be used to make this even smoother, by using a circuit to "regulate" the supply voltage down to a lower voltage, but one which has even less ripple (and no sag, within limits). Some designers use them, some don't. Why a tube one might or might not be better, I couldn't say.
Do be careful not to make assumptions on the sound of a component from certain parameters of its circuit design. That way lies madness.