White has significance in several cultures, many of which attach similar meanings to the color. The most popular associations include purity or cleanliness. We see this in the cultural tradition of America and other countries of a white wedding gown, symbolizing the purity of a virgin bride. Similarly, in Judeo-Christian tradition, characters thought of as pure are often represented in white robes, i.e. saints, angels, Jesus, etc.
These visual representations often lead to another association of the color, which is innocence. Again, this has religious significance, esp. in Judeo-Christian societies, but within the greater community white often involves an absence of evil, and therefore an abundance of innocence.
Finally, white can also be a symbol of death. This is the closest association in Fahrenheit 451. The idea of innocence/purity plays into this, as in death, one is cleansed of sins. See also Whitman's "A noiseless, patient spider."