There are several approaches, when starting your own startup.
Most startups these days are using the approach of 'we build a great product, and users will come'. They begin with a vision, or a problem that needs a solution, and then build their service.
Some startups, however, take a different approach. These startups work mostly in the enterprise (B2B) arena. They actually begin as a one project company, and build their product for one customer. Then they refine, it as more customers come in.
The product approach is more common, because you don't have to do much as an entrepreneur - Just explain your vision, and if it makes sense (And you have some connections), you'll get some funding to begin. You can sprint your product, and then launch, and hope (Or use PR/ Community managers/ Marketing) to generate buzz and acquire users. Sometimes (Like, um, a lot of successful social companies) the product becomes a hit, and then you worry (Or not... Like Instagram) about monetizing it.
The project approach is harder. You need to partner with one (Or few more) customers, which will also pay you for your service (That doesn't necessarily exist yet). And then you have to deal with them, and all the growing pains of sorting out the problems. However, you might not need funding at all - This means, with current valuations and VCs pressing entrepreneurs desperate to keep their dream alive, that you might not need that phase at all. After you gain enough customers, you'll have a sense of what the market needs, and you can actually build a working product.
And then there's another approach.
Find a targeted person (Or small audience) for your idea, and build the product for him. (Or her... I'm using male for comfort reasons only) Treat him as a paying customer. Each one of your audience should be treated as a 'project'. Then you can actually get the real sense of what your product should be.
Finally, here's a great product that succeeded mostly because the developers that built it did it for a great audience: Themselves. I wrote about MongoDB in previous posts, here's an explanation of what makes this product so popular:
http://blog.mongolab.com/2012/08/why-is-mongodb-wildly-popular/
