Mfcttrf

Under "Moving Between Attacks" it says:

"If you take an action that includes more than one weapon attack, you can break up your movement even further by moving between those attacks..."

If you were to twin booming blade then this would be an action that includes more than one weapon attack. Does this really mean you are able to move between the two attacks of a twinned booming blade?

Note that Twinned Spell requires you to

"target a second creature in range with the same spell"

so, to me, even if this is possible, you could not move particularly far using this method as both targets need to be in range when you cast the spell.

Yes

The effects of booming blade, which are twinned with meta magic does exactly what it says twice:

As part of the action used to cast this spell, you must make a melee attack with a weapon against one creature within the spell's range, otherwise the spell fails.

The general rule reads:

If you take an action that includes more than one weapon attack,

Both of those are satisfied. So You can indeed do the then clause of the general rule:

you can break up your movement even further by moving between those attacks...

How far?

There isn't a limit (aside from your speed) to the amount you can but, but Twinned Spell requires you to target a creature in the original range of the spell:

target a second creature in range with the same spell

So you can move your total movement between the two, but the second attack has to be within the spell range (5ft) of the first target. So if you had a speed of 30 you can move 15 feet away, turn around and move 15 feet back and attack someone in the original range.

Booming Blade States:

As part of the action used to cast this spell, you must make a melee
attack with a weapon against one creature within the spell's range

And Twinned Spell:

When you cast a spell that targets only one creature and doesn’t have
a range of self, you can spend a number of sorcery points equal to the
spell’s level to target a second creature in range with the same spell
(1 sorcery point if the spell is a cantrip).

To be eligible, a spell must be incapable of targeting more than one
creature at the spell’s current level.

And as you stated in your question, Moving Between Attacks:

If you take an action that includes more than one weapon attack, you
can break up your movement even further by moving between those
attacks.

By Twinning Booming Blade, you would be able to target a second creature, which would cause you to have a second melee attack. Since you would have a second melee attack, you would be able to move between the two.

So I would say yes, you would be able to move between the regular and Twinned attacks of Booming Blade.

Further, since Twinning allows targeting a second creature, but not a free casting of the spell, you would need to be within range of both targets at the time of casting.