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Burn It! increases fire damage:
Your spells and alchemical items that deal fire damage gain a status bonus to damage equal to half the spell's level or one-quarter the item's level (minimum 1).
Wildfire does fire damage per square:
A creature that moves on the ground through the area takes 1 fire damage for every square of that area it moves into.
Is the combined damage increase per square?
Burn It! works on spells that deal fire damage and Wildfire is a spell that deals fire damage. Thus, the Wildfire spell gains a bonus to its damage, which happens each time somebody enters a Wildfire square. Thus, they take more than 1 damage for each square.
Supporting that increasing the per-square damage is even possible is the Heightened effect of Wildfire itself:
Heightened (+2) Increase the damage and persistent damage by 1.
"The damage" is the per-square damage so when Burn It! similarly increases the damage, it is increasing this per-square damage.
