A lot of websites don't open their services for everyone. They claim that their sites are in "beta-phase" and that's why they give away invites only to some people, because they don't want to overload their servers. But that's only one side of the truth.
The other one is, that invites are a marketing-instrument, which works in two ways:
What costs nothing, is worth nothing
The old wisdom is also right for online-services. By restricting the access to a service, people get curious about a new product. An invite is valuable, because not everyone has one. Thus, the service is more valuable. That goes hand in hand with the second marketing-mechanism of invites: Word-of-Mouth.
Word-of-mouth: Blogs and Forums
Bloggers blog about invites. Once your are invited to a service, there is the possibility to pass more invites to other people. Invites give people a reason to make a post about your product in their blog. You know those posts: "First 5 comments get an invite". Bloggers would do everything for a comment... Furthermore there are a lot of forums where people open new threads to pass invites to each other.
Those posts in blogs and forums have two implications:
They result in precious links to your website (Search Engine Optimization) and
more people knowing about your product (free advertising!)
The first service that I can remember, that used such an invite-marketing-model was GMail. People were crazy to get invites. Nowadays it's a standard-model to introduce new services to the web-community.