What William Faulkner means by this quote is that internal conflicts are a better basis for a story than external ones.
The Meaning of the Quote
Faulkner was suggesting that the basis of good fiction - be it poetry or prose - comes from within, and that internal conflict is the foundation of the most important pieces of literature. This doesn't mean that external conflicts aren't important; rather, it suggests that they are important, but it's how the characters deal with them that makes a good piece of fiction. This is because writing that reaches the reader on an emotional or spiritual level is very powerful, and will linger in the mind far longer than writing that deals solely with external conflicts.
For example, man vs. Zombie is only powerful for the emotional or internal struggles that it usually entails; if a character has to kill his best-friend-turned-zombie, the emotional torment that the character faces has more of an impact on the reader than the mere fact that there are zombies. If the hero's brother dies because of the hero's reluctance to kill his zombie best friend, then this is where the novel's 'heart' is at.
The Quote in Context
The quote comes from a speech Faulkner made in 1950, after receiving the Nobel Prize for Literature. The quote in full is as follows:
"Our tragedy today is a general and universal physical fear so long sustained by now that we can even bear it. There are no longer problems of the spirit. There is only the question: When will I be blown up? Because of this, the young man or woman writing today has forgotten the problems of the human heart in conflict with itself which alone can make good writing because only that is worth writing about, worth the agony and the sweat. He must learn them again."
About William Faulkner
Born in 1897, Faulker was a prolific American writer, best known for novels such as The Sound and the Fury (1929), As I Lay Dying (1930) and Light in August (1932). He also wrote short stories.