Uber solves a problem. You always needed a reliable way to get from a to b, and Uber does that, in many ways better than a cab.
Lady Gaga solves a problem. You have neophilia when it comes to music, and she'll bring you new music to satisfy your curiousity.
Same thing goes for Zara. They solve the 'what's new in fashion' problem for a lot of early adopters.
On the other hand, Uggs created a problem for people who aren't necessarily fashion forward but want to wear what everyone else is wearing. Once "everyone" was wearing Uggs, these fashion-laggards had a problem—if they wanted to keep up, they had to go buy a new pair of boots.
In most successful business-to-business selling, the big wins come from creating problems. Once the competition is busy using your new innovation, the other companies have to buy it to keep competitive. Once other brands are using your social medium, the laggard brands do too—not because you've solved their problem, but because you've created one. The people in a traditional bureaucracy buy something new when they have to, not when they want to.
(It's interesting how we recoil from the idea of creating problems. Of course, progress is about creating opportunities, and opportunities always bring along their close colleague, problems.)
Or consider the case of a non-profit seeking to raise funds or gain government support. Without a doubt, they have to create a problem in the mind of the donor, or there will be no funds or no support to solve that problem.
It is clearly more fun (at first) to solve problems because everyone is happy to see you and the discussion is simple indeed, "You know that problem you used to have? We just solved it." The innovations that change the world, though, often create (or highlight) problems before they solve them.
[HT to Mo for the title]