An Innate Spellcaster casts bonus spells each round, if they aren't unconscious. These can be any spells they are able to cast and have the gems for. They do it "innately"; that is to say, without any actions that may take time or be interrupted.
What causes an Innate Spellcaster? Most are Pretender Gods, particularly those of the top row (also known as "Idols"); these typically have a form that serves as a vessel for something else, which doesn't move its form under its own power despite being connected to it. The Mallquis of Nazca fit in this bunch. Then there are the entities with multiple minds or wills within them, one or more of which can cast spells while the other(s) focus on movement; these are a good deal rarer. Some are both.
According to the manual, Innate Spellcasters don't prepare spells at all, and they can't be interrupted because the opportunity never arises. The manual also says they disregard changes in casting times. For reference, a spell with "100% Casting Time" takes around half a round to prepare to cast, and then another half of a round to recover from. A "200% Casting Time" spell would require a full round to prepare to cast and then another full round to recover from, but not for Innate Spellcasters: they cast the spell immediately, and then wait the standard half-round to recover.
According to testing in Dominions 5, Innate Spellcasters work differently. As suggested by the manual description, their first spell comes out immediately when the battle starts; from there, each of their spells has the typical 100% Casting Time of non-Innate Spellcasters (though in complete disregard of their actual Casting Times), except that each bonus spell operates on their own cooldown. They never get interrupted by damage because a special rule says they can't be. Their spell preparation doesn't prevent them from moving or attacking.
If an Innate Spellcaster is in a Communion/Sabbath/Chorus, they may not be a Slave in it. Spells cast by an Innate Spellcaster generate twice as much Fatigue for their Slave underlings, simply due to the disconnect between the caster and their slow-rhythmed supporters.