From MetroAmp Wiki
A vacuum tube amplifier B+ and bias supply must have a filter circuit. This is because the AC to DC conversion job of the rectifier actually produces "pulsed DC" rather than a steady DC voltage. Pulsed DC is not usable since its value is always changing in amplitude. On top of that, the "ripple" of pulsed DC will introduce noise into the audio signal path.
Below is an example of "pulsed DC".
As you can see, there is a time period where the voltage of the power supply is falling, then rising back to its peak again. We need to somehow devise a circuit that can temporarily supply power to the powered circuit (i.e. the amplifier circuitry) while this is happening to get rid of the gap in power supply voltage caused by the falling and rising voltage. This is the job of the filter circuit.