Evocation is a flashy form of magic that has fires, explosions, etc. It is first mentioned in Storm Front.
This type of magic is what is mainly used in direct combat situations. The ability to use it without ritual allows more focus on combat than anything else. It usually works best with a focus depending on the skills of the wizard. While it takes a while to learn a new evocation, it has the advantage of being able to be used on the fly.
Harry Dresden calls it "Quick and dirty" magic. It draws directly from the wizard's will and is turned loose without benefit of a guide or limit. It is dangerous and difficult and is useful for throwing around a lot of energy.
Dresden does not consider himself good at evocation because he does not have a lot of finesse. There are few who can control it properly and reliably. Donald Morgan was one of deadliest evocators in the world.
Phonoturgy is an unusual form of evocation, in that it's somewhat more muted than usual. It's helpful in situations where stealth is required, such as battle situations or sneaking upon one's enemies.
In the series
In Storm Front, Harry Dresden tells Karrin Murphy and Ron Carmichael the two possible ways that the murder victims, Jennifer Stanton and Tommy Tomm, whose hearts had exploded out of them, could have been killed by magic: Evocation or Thaumaturgy.
In Proven Guilty, Harry Dresden invents a new evocation on the fly when trying unsuccessfully to escape the Scarecrow fetch in a high speed chase. Dresden tossed water bottles tossed from the Van, heated them until they exploded their water out, then used an intense flame to draw the heat out of the area, freezing the puddle. The Scarecrow fell on the ice giving Dresden and Thomas the chance to escape.
In Ghost Story, Harry Dresden's ghost attempts evocation spell of fire powering it with his memory of when he shot a Loup-garou through the wall of Murphy's police station. It passed right through the Fomor servitors sent by the Leanansidhe to test Molly Carpenter's combat skills that she's been teaching her.