This is the 11131st most frequent Russian word.
горящему
The Russian word "горящему" means "to the burning (one)" or "to the flaming (one)" in English, depending on context.
In this sentence, 'горящему' is used as an adjective in the dative case to describe the campfire ('костру'). It implies the fire's state of burning at the moment.
Я подошёл к горящему костру, чтобы погреться.
I approached the burning campfire to warm myself.
Here, 'горящему' again acts as an adjective in the dative case, providing a description of the house ('дому'). It denotes that the house is on fire.
Вместо помощи горящему дому, они смотрели на него.
Instead of helping the burning house, they were watching it.
In this instance, 'горящему' functions as an adjective in the dative case modifying 'человеку'. It signifies the person's condition of being ablaze.