This quote is taken from Part Two of Fahrenheit 451, when Montag and Faber first meet in the park. In terms of its meaning, this quote reflects Faber's attitude to life: he believes in the value of thought, in pondering life and its meaning, not simply accepting things at face value.
Notice how Faber contrasts with a character like Mildred, for whom life is about "things:" driving fast and watching the parlor walls, for instance. These are mindless activities which require no thought, just a passive involvement. Faber is the complete opposite: for him, life is about thought and this is why he loathes censorship so much. He knows that books are valuable, not for the words they contain, but because books encourage people to think critically about their lives.
Because Faber looks for meaning and engages critically with the world, he feels "alive." In other words, he uses his mind to its full capacity, instead of accepting what he is told by the government without question.