To lust after something is to want something very, very much. You might lust after a person, but we use this verb more often with things that we would like to possess, like a car, a handbag, an iPad. If just thinking about the thing makes your mouth water, you lust after it! Advertisers and marketers have the challenge of making us lust after things, and I think this is a difficult job, especially when there are so many things to choose from!
Right now in Barcelona, we're having the big winter sales, which give people (the quick ones, anyway) a chance to buy things they've been lusting after but couldn't afford before. New coats, boots, nice sweaters, etc. Personally, I'm not really lusting after much these days, but you never know when I might see the perfect leather jacket... What about you? Are you lusting after anything right now?