Why is ballroom dancing important to Sam and Willie in "MASTER HAROLD" . . . and the Boys?

Sam and Willie regard ballroom dancing as important because it represents life perfected. When he is speaking about the perfection of the dance floor, Sam explains to Hally, "There's no collisions out there, Hally. Nobody trips or stumbles or bumps into anybody else." He goes on to say that being a finalist in a dance concert is like living in "a dream about a world in which accidents don't happen." At the beginning of the play, Sam lectures Willie about the importance of Willie's pretending to like Hilda, his dance partner, even if he doesn't feel romantic about her, to create the picture of perfect romance. In reality, Willie beats Hilda.

To Sam and Willie, ballroom dancing represents the unattainable and easy way of getting along with others that they cannot have with Hally, for example. They want to glide along effortlessly in their relationship with Hally, who they have known for a long time, but Hally treats them with disrespect by spitting on them. Sam and Willie had hoped to guide Hally to adulthood in a graceful way, but Hally's sense of entitlement, displaced anger against his father, and racism make this type of beautiful relationship impossible. Instead, Sam and Willie can only find beauty and a collision-free existence in ballroom dancing. 

In "MASTER HAROLD" . . . and the Boys, why does Sam value ballroom dancing?

As well as seeing it as an escape from his humdrum, impoverished existence, Sam looks upon ballroom dancing as a metaphor for a better, more harmonious world. As he tells Hally, with ballroom dancing there are no collisions; no one trips or bumps into anyone else. Everyone happily does their own thing without causing any trouble.

Contrast that with South African society under apartheid, which is rigidly divided along racial lines. In metaphorical terms, this is a society in which people regularly bump into each other, i.e. are in constant conflict with one another. And it's the same in the world as a whole. The current state of international politics means that the United States is regularly "bumping into" Russia, England into India, and rich men into poor men. As Sam points out, people get hurt in all that "bumping." If only life in South Africa and the rest of the world could be like a ballroom dancing contest, everyone would live in complete harmony.