This is an example of a metaphor.
Figurative language uses figures of speech to be more effective, persuasive and impactful. They give readers new insights, expand the readers' interpretations and broaden their imaginings. In other words, they appeal to the senses of the readers.
Figurative language is common in literature and poetry. Some of the devices of figurative language are: alliteration, hyperbole, metaphor, personification, simile and symbolism.
<em>A metaphor</em> is a comparison between two things. They have to make a link in the reader's mind.
<em>The cup of endurance runs over</em> is a metaphor as it compares the cup with a measure of time. As the cup runs over so does the time finishes. This metaphor, written by Martin Luther King Jr, refers to the experience of racial intolerance. Racial intolerance could only be lived with for a limited period of time after which the situation will/must change.