Factors that break wudhu

Making wudhu after eating food cooked on a fire

Q: There is this book called "The Tablespread Of the Holy Prophet" written by Muhammad Faisal

There is a section on cheese. This hadith is a Sahih Muslim Hadith 687, Narrated by Abu Hurayrah (radhiyallahu anhu).

"Performing ablution in the mosque, he said: I am performing ablution because of having eaten pieces of cheese, for I heard the Messenger of Allah Ta'ala say: Perform ablution (after eating anything) touched by fire."

I would like to know what is meant by "touched by fire" and why should we make wudhu after eating something that is touched by fire?