Burn stain on unknown countertop material
This appears to be a laminate such as Formica, which cannot be repaired from heat damage. Your only option really is to replace the affected portion, either with another piece of Formica or with some kind of insert like a cutting board, trivet, etc.

You might also be able to put a new layer of laminate over top. 

This video from This Old House shows some methods for replacing the affected portion.