Normally, spontaneous spellcasters are unable to use Quicken Spell due to the fact that spontaneous spellcasters increase the casting time for spells when they use metamagic. Every spontaneous spell that has metamagic applied to it takes a minimum of a full-round action, which defeats the purpose of Quicken Spell. The Quicken Spell feat specifically calls this out, and thus clarifies that the increased casting time has trumps the effects of Quicken.
This feat can’t be applied to any spell cast spontaneously (including sorcerer spells, bard spells, and cleric or druid spells cast spontaneously), since applying a metamagic feat to a spontaneously cast spell automatically increases the casting time to a full-round action.
So Metamagic Specialist (and the Rapid Metamagic feat in Complete Mage, which is massively superior) eliminate the increased casting time. With no increased casting time, there is no reason why Quicken Spell shouldn’t work, but since the rules for Quicken Spell call out spontaneous spells specifically, Metamagic Specialist and Rapid Metamagic have to as well. That is what Metamagic Specialist is doing here.
This does not give you the Quicken Spell feat, does not allow you to apply the Quicken metamagic without the feat, and does not make it free to apply Quicken to any spell. It literally just undoes the rule that says spontaneous casters cannot use Quicken Spell.
As an aside, the increased casting time for spontaneous spellcasters using metamagic is awful, and I highly recommend houseruling it away.