"the ability to laugh heartily is, in part, the salvation of the american negro; it does much to keep him from going the way of the indian"
The narrator is saying that the ability to laugh at life's troubles has helped the "Negros" to survive through slavery and systemic racism through the years. He juxtaposes Negro survival with the Native Indian genocide that nearly wiped out the native population when the Europeans conquered the American continent. The narrator implies that the natives might have better survived if they had a sense of humor like black Americans.
