Spellbinder's second ability allows you to create a copy of the imprinted instant card in the Exile zone (that's where the imprinted instant card is) and then cast it without paying its mana cost.

Spellbinder imprints a card only once, when it enters. Attaching Spellbinder to a creature doesn't trigger its "enters" ability.

You don't pay the spell's mana cost. If the spell has X in its mana cost, X is 0. You do pay any additional costs for that spell. You can't use any alternative costs.

If the copied card is a split card, you choose which one side of it to cast, but you can't cast both sides. You can choose the other side later in the game, though.

The creation of the copy and then the casting of the copy are both optional.