Free form casting means that you don't know a spell (Spells Known), but it's on your list. Let's say you're a low-level hedge-wizard summoner and you have Summon Monster I (Celestial Dog), Summon Monster I (Fiendish Raven) and Unseen Servant as your Spells Known. (Not worrying about numbers right now--let's say Spells Known: 3 1st and roll with it.) You can try free-form casting to summon a Fiendish Octopus, or a Dire Rat (SNA I list), or whatever skeleton you get for Summon Undead I. You're a summoner, you summon things. You're taking a risk and going outside your comfort zone (chance of failure, backlash damage), but it's not completely out of your area of competence. You can't just free-form cast magic missile or shield or charm person, and you just don't have the power to summon something from a higher level list.
IF you're a book-wizard, and you want to cast a spell, you need to have access to that spell in a spellbook. A spellbook isn't just one wizard's personal idiosyncratic collection of spells--it's a stable batch of spells united by a theme and known by a name (Necronomicon, LEsser Book of Changes, Greater Book of Changes, Compendium of Conjuration, Testament of HErmes Tristigatus, etc). Or you have to use the individual-research rules. You're a book wizard, so no book no spell. (You can cast your Spells Known without a book, because you've internalized those spells by studying them in--books.)
I'm still working on what advantages specialist casters get. On the one hand, they lose a lot of versatility compared to book-wizards. On the other hand, PC specialist will create Tier 4 ubercharger problems, where there is no "sweet spot" of difficulty where challenges are difficult but still manageable.