The above comes from the following full paragraph spoken by Martin Luther King, Jr.:
The ultimate measure of a man is not where he stands in moments of comfort and convenience, but where he stands in times of challenge and controversy. The true neighbor will risk his position, his prestige, and even his life for the welfare of others. In dangerous valleys and hazardous pathways, he will lift some bruised and beaten bother to a higher and more noble life.
Essentially, King is arguing that a man's true worth is shown when he takes action in times of difficulty. As a minister, he also refers to the biblical requirement for people to sacrifice their lives for each other and lift each other up out of times of trouble. King lived during a time of significant racial oppression and a time of fighting against that oppression. His reference to "challenge and controversy" points to the fight for equal rights and enfranchisement he helped lead African Americans in during the 1950s. His reference to sacrificing one's life for the "welfare of others" speaks of all the literally life-endangering sacrifices African Americans and whites made to achieve greater equality for the African Americans. Furthermore, his phrase "lifting some bruised and beaten brother" points to all of the physical, emotional, and psychological oppression African Americans suffered throughout the ages and the need to finally lift our brothers up from that oppression.
One example of the historical circumstances surrounding his spoken paragraph is the historic Montgomery Bus Boycott. Montgomery, Alabama, like all of the South, was a heavily racially segregated area, and African Americans were forbidden to sit on the bus among the whites. In December 1955, Rosa Parks was arrested for refusing to yeild her seat in the black section of the bus to a white passenger after the white section had been filled up. Her arrest sparked a bus boycott by African American citizens that leaders intended to use to call attention to racial discrimination. Boycott leaders, like King, planned for the boycott to last only one day, but it lasted 381 days instead. Soon, whites retaliated using violence, even bombing King's home, showing us what a violent and oppressive time King lived in when he spoke these words.