what does a Rectifier tube do?

A rectifier tube (diode) changes alternating current into little lumps of direct current. See

www.electronicstheory.com/html/e101-39.htm

I remain,

To answer the question: A rectifier (or rectification) is anything that allows something to flow in one direction without hindrance, but not the other. Its possible for a loudspeaker's port to start acting as a rectifier: air doesn't flow out as easily as it does in, or vice versa. I believe its called a full-wave bridge rectifier that's used in solid-state to convert AC (alternating current) into DC (direct current).

I've no clue about Mullard rectification but I have two assumptions that the second diode tube either rectifies a phase inversed signal or the split-phase signal(where one phase is lagging bihind another by 1/2period making a twice as freequet "lumps" that are much easier to smooth up with capacitors that have proper time delay. Inverting phases as well as splitting phases can be done using a transformer.

thanks for the input so far.....the AirTight 1 (which I really think is the best tube amp Ive heard) uses 2 5ar4 rectifiers.....the AirTight 3 which is an amp Ive have always lusted after uses the same output tubes (el34) and input tubes, but does not use 5ar4 rectifiers. Each amp uses same transformers, point to point wiring and exact parts, Would the amps sound the same or in what way would the Atm1 differ sonically vs the Atm3 because of the lack of the rectification?

you might want to try searching on Audioasylum, either under General or Tube Asylum.

I recall reading some interesting stuff there re: tube rectification and it's effects on tube "bias" setting (fluctuation more likely with tube rectification)Some dude had modified am amp to enable him to plug in a solid state rectification device into the tube sockets...
Also, from my own experience (manufacturer hype) AudioPrism Debut I used to own had pretty good bass for an EL-34 based amp, due, in part (according to manufacturer) to the solid state rectification (no tubes used for this purpose).

Then again, I just compared a Tube Rectified Cary to a SS rectified Rogue, and the Cary had stronger bass (but the tubes did fluctuate a bit, however the audible effects of tubes fluctuating by 2-3% are unknown to me).

Anyway, I really don't know. But (this sounds silly) in my experience, the more tubes used for ANY purpose, the better the sound(and the worse off your wallet will be).
good luck.