I will try to guess here, ok? I think informal definition is like the meaning of the word in your own words, like the word pencil means something you use to draw or write. Then the formal definition is the actual definition that you can find in the dictionary. According to dictionary.com, the word pencil means "A slender tube of wood, metal, plastic, etc., containing a core or strip of graphite, a solid coloring material, or the like, used for writing or drawing."
But I really don't know what an amplified definition is. Sorry! :(