It's act 2, scene 2 of Macbeth, and Lady Macbeth is all excited at the imminent prospect of her husband murdering King Duncan and taking the throne of Scotland for himself. The servants supposed to be guarding Duncan are blind drunk, and Lady Macbeth is positively intoxicated by the same alcohol that they've drunk; it makes her feel incredibly bold. What has quenched them has given her fire.
Just then, Lady Macbeth hears the shrieking of an owl. According to ancient folklore, this was a sign of someone's imminent death. Lady Macbeth certainly interprets it that way, believing that it means that her husband is “about it”—in other words, that he's in the process of murdering Duncan.
According to Lady Macbeth, the owl is like a bellman, a crier who rings a bell to announce someone's death. In Shakespeare's day, bells would also be rung at someone's funeral, and so the very mention of a bell at this critical juncture in the play reinforces the sense that death is in the air.
The blood-curdling shriek of an owl is particularly appropriate in a play jam-packed with supernatural elements. Although the owl is very much a creature of this world, the piercing shrieks it emits seem to come from a different world entirely: the supernatural world partly inhabited by the Weird Sisters.