EBay solved the problem of people needing a place to conduct safe, private party transactions.
Facebook solved the problem of MySpace being clogged with spam (get your free iPhone now!)
Groupon solved the problem of empty spas and sushi going bad.
I kid Groupon and Facebook, but the idea has merit. iScripts.com did over 200 individual software projects last year and almost all them solve a problem of some shape. Just off the top of my head, I had a client who created a marketplace for ordering entire crops of farmers produce, another who is creating a marketplace for their local area to support local commerce, and another who wants to set up a marketplace to trade sports jerseys and shoes. Each of these marketplaces solve a problem that has commercial value to those who need a solution.
The moral of the story here is that if you can quickly identify what the core problem is that you solve, you can better target the market who has that specific problem... and then market to them.
I don't want to end the blog post on a bad note, but if you want to start your own website and you cannot answer this question, you may be in trouble already. I meet people all the time who want to start a social network or a dating website, but they do not have a focus for who they are trying to market to or what problem they are trying to solve with their start up. I never discourage them, because you never can tell where lightning will strike next, but if one tries to start a generic social network they are essentially dooming themselves to compete directly with Facebook. Is it possible to do so? Absolutely. But you better have really deep pockets if you want to play in that league.
To take a minute, think about what problem you're solving and that help you to determine your niche market and your path to success.