le désir brûlant translated to English means "The Burning Desire". The burning desire is like a fire inside of you, driving you full force to do something. It's either get there or die trying.

Briefly, "the realization that each random passerby is living a life as vivid and complex as your own." Originally from the Dictionary of Obscure Sorrows, which has a lot more beautiful neologism definitions like this you might enjoy.