This is rather an old-fashioned word. It means 'to want to possess', 'to desire', 'to lust after' - with a strong idea that this is the bad longing for something that leads to theft, or other immorality. Its principal connotations to traditional European Christians come from the Authorized Version of the Ten Commandments: "Thou shalt not covet thy neighbour's house, thou shalt not covet thy neighbour's wife, nor his manservant, nor his maidservant, nor his ox, nor his ass, nor any thing that is thy neighbour's."
The adjective covetous is used to mean 'very desirous', or even 'jealous', of something. "He has the latest i-pod - I am so covetous."
- You may also want to see covert.