What is exactly meant by "Material rebirth lust", and how is it properly abandoned?
The Pali is rūparāgo. 'Rūpa' means 'materiality' and 'rāgo' means 'lust'.
It is lust for rupa jhana, i.e., 1st, 2nd, 3rd &/or 4th jhana.
It is not lust for 'rebirth'. The word 'rebirth' is not found in the Pali.
It is abandoned by the destruction of lust & clinging, i.e., Nibbana.
It is abandoned as follows:
Take a mendicant who, quite secluded from sensual pleasures, secluded from unskillful qualities, enters and remains in the first absorption. They contemplate the phenomena there—included in form, feeling, perception, choices, and consciousness—as impermanent, as suffering (unsatisfactory), as diseased, as an abscess, as a dart, as misery, as an affliction, as alien, as falling apart, as empty, as not-self. They turn their mind away from those things, and apply it to the deathless: ‘This is peaceful; this is sublime—that is, the stilling of all activities, the letting go of all attachments, the ending of craving, fading away, cessation, extinguishment (Nibbana).’ Abiding in that they attain the ending of defilements.
The 6th fetter's meaning pretty straightforward: the craving for the fine-material (or form) existence/Rupa-Raga. The lower 5 fetters are lower because they're all related to our world, which is the sensuous world (Kama-Loka), while the 5 higher fetters are those that are tie to the 2 higher worlds above Kama-Loka: Rupa-Loka (form or fine-material world), and Arupa-Loka (or immaterial world) (see Planes of Existence and RupaRaga for further details).