The poem's title lets readers know who the speaker is: the wife of Sisyphus, a king in Greek myth known for his attempts to outsmart the gods and cheat death. When the gods discovered his trickery, Zeus sentenced Sisyphus to an eternity of rolling an enormous boulder up a hill. As soon as Sisyphus neared the top, the boulder would roll back down, thus ensuring he could never actually complete his task. (This is why people refer to difficult yet futile tasks as "Sisyphean"!)
This poem is told from the perspective of Mrs. Sisyphus, however (whose name in myth was Merope). And even as the poem draws on ancient myths, its language is distinctly contemporary and conversational—the first hint that Duffy is reinterpreting the story of Sisyphus and Merope to make a point about modern life and work.
The poem itself opens with Mrs. Sisyphus pointing her husband out to an unseen listener nearby, saying, "That's him pushing the stone up the hill, the jerk." Right away, it's clear that she's far from thrilled with her husband's choices! She then uses a simile to compare the "stone" Sisyphus is pushing to a "kirk," or church. This comparison suggests just how enormous this rock is, and it also implies just how devoted Sisyphus is to pushing that rock up the hill. It's as if he worships his work or treats it as a holy calling.
He's clearly been at it for a while, too: his wife goes on to say that back when Sisyphus first started with this rock-pushing business, his intense commitment "just used to irk," or mildly annoy, her; now it "incenses," or enrages, her. Perhaps that's because she understands that he's never going to succeed—that the stone he pushes will just keep rolling on down the hill. Having lost patience with his commitment to a pointless task, she calls Sisyphus a "berk" (or a dunce) and adds that she could "do something vicious to him with a dirk" (a dagger). In other words, she's so angry she'd like to attack him with a knife.
This is a violent image, to be sure, but the poem's language keeps things feeling light-hearted. The poem is written in free verse, so it doesn't follow a regular meter or a rhyme scheme. That said, it's filled with playful rhymes: in the first stanza, for example, every line ends in a full rhyme ("jerk," "kirk," "irk," "berk," "dirk"). The wealth of sharp, biting /k/ sounds evokes Mrs. Sisyphus's bitter disgust with her husband. The heavy use of single rhyme sound also echoes the repetitive nature of Sisyphus's task. Finally, these are all rather funny sounding, unusual words, and their presence adds to the poem's playful feel.