Muggles' Guide to Harry Potter/Magic/Priori Incantatem

Overview
Rather than a spell, Priori Incantatem is an effect that occurs when two wands that have magical cores deriving from the same source are used against each other. One or the other of the wands is forced to regurgitate the last spells that it was used to cast. The effect is very similar to the spell Prior Incantato.

Extended Description
This effect is seen near the end of Harry Potter and the Goblet of Fire during the graveyard battle between Voldemort and Harry Potter. Both Harry's and Voldemort's wands are powered by tail feathers given by Fawkes. When they simultaneously cast spells at each other, this effect appears. A fiery stream joins the two wands, forming a golden light that envelops Harry and Voldemort; there are fire beads on the stream between the two wands, which Harry thrusts backwards into Voldemort's wand, forcing it to disgorge its past few spells. The spirit "echoes" of Cedric Diggory, the muggle Frank Bryce, Bertha Jorkins, and Harry's mother and father, who were the last people murdered using Voldemort's wand, appear as ghostly simulacra of their living selves.

Greater Picture
We learn much later that this also has the effect of transferring some of the powers of one wand into the other. In this case, Harry, being the stronger wizard for reasons that are discussed elsewhere, manages to force Voldemort's wand to disgorge its most recent spells, and in the process gains some of the power of Voldemort's wand.