This is the 4577th most frequent Russian word.
горящего
"Горящего" means "burning" or "on fire" in English.
In this sentence, "горящего" is a present participle derived from the verb "гореть" (to burn), describing the metaphorical burning characteristic of enthusiasm.
Я увидел человека, горящего энтузиазмом.
I saw a person burning with enthusiasm.
Here, "горящего" is again a present participle acting as an attribute for the noun "дома" (house), indicating the current state of the house being on fire.
Пламя горящего дома было видно издалека.
The flames of the burning house could be seen from afar.
In this usage, "горящего" describes the participle form of the noun "костра" (campfire), relating its ongoing action of burning.