A few figures of speech could fit this famous line from Othello. Depending on the translation (I'm assuming it's accurate) and the stage action (the way the line is delivered on stage), it could mean any of the following:
Aposiopesis -- Breaking off as if unable to continue: “The fire surrounds them while—I cannot go on.” Othello is telling Desdemona to put out the light (of her candle and *life*), but he can't bring himself to say it literally and directly, so he just repeats himself metaphorically.
Puns (Paronomasia) -- A pun twists the meaning of words, often to create an ironic, humorous effect. "Put out the light" could mean to put out the candle and to be extinguished of life. He seems to direct the first half of the line to Desdemona and the second part to himself, as if to summon up the courage to kill her.
Diacope (also called Epizeuxis)-- Uninterrupted repetition, or repetition with only one or two words between each repeated phrase. ("The horror! The horror!") He's simply repeating it for memorable effect. The anaphora (of sorts) becomes more dramatic upon repetition.
The first part of the sentence is literal. Othello is actually referring to putting out the light of a candle. The second part is metaphorical. Putting out the light is a metaphor for the killing of Desdemona. Othello compares the two. A candle can be relit. Once Desdemona's light is put out, her life cannot be restored. Killing her is irrevocable. Othello is quite conscious of the gravity of his action.
But "light" is also a symbol. Throughout the play, light symbolizes Desdemona and her goodness. She, for instance, vows by "this heavenly light" that she will not cheat on Othello, while Emilia jokingly declares that she would in the dark.
When Othello chooses to kill Desdesmona, he is in essence destroying the light in his life. He has joined forces with "hell and night" and fallen into Iago's monstrous trap, and now "chaos has come again."