Othello says “Put out the light, then put out the light” to himself in the form of an imperative sentence. The stage / room is dark. He commands himself to do this while bending over and kissing a sleeping Desdemona. In preparing to kill her, he puts out the candle (the “flaming minister”) in their bedroom, hiding his actions in darkness out of shame. The “light” also refers to Desdemona, signifying her skin, which is “whiter … than snow” (5.2.4), and her character, which is pure, in contrast to his dark skin and his sins of jealousy and pride as well as the sin of murder he is about to commit. The way in which Shakespeare presents Othello in shadows and obscurity in this scene, as well as others, makes us associate him with the night, combining the black shadows of dusk and the colour of his skin to make us more unsure of the man when the scene is set at night. Besides characterizing himself and Desdemona, in these lines Othello is also satisfying his tragic fate by ‘putting out the light’ on her, then later himself. Othello knows and feels the difference: he realizes that Desdemona is “a pearl richer than all of his tribe ”(5.2.347). The light of this treasure established his standing in Venetian society, and he now is nothing but the old black ram,” (1.1. 87) “the “circumcised dog” (5.2.355).
This line is Othello's, 5.2.7. He is referring to his imminent murder of Desdemona. He comes to her room while she slumbers, holding a candle. He will kill her in the dark, literally, and "put out her light," her life, metaphorically.
If you back up one line, the statement makes a bit more sense. Othello is convinced of Desdemona's betrayal. He wants his own revenge, but also feels that she must die, "else she betray more men."
Othello is literally putting out the light of the candle and then poutting out the light of Desdemona's life. The light of Desdemona's life, however, is also an allusion to Prometheus of mythology. Prometheus breathed life into clay figures (giving them the light of life), and he also brought fire from the gods to man. Thus the "light" in reference to Desdemona's life is also an allusion to Prometheus' light.