The premise behind Meezoog is that relationships aren't simple. All - or most - other social networks don't differentiate different types of relationships much; you "friend" people and then they're all your "friends." Meezoog, however, lets you define relationships in detail: Ann, for example, can be a close childhood friend, whom you're meeting with at least once a month, while John can merely be a neighbor you've met 6 months ago and whom you occasionally bump into.
That's not all. Meezoog has employed an algorithm that calculates "trusted paths" between people. When you do a search, you get results ordered by "social proximity" - the ones that deserve your trust the most will be on top.
Finally, it's important to understand that Meezoog is not the most important product here; it's just one social network that employs the technology called TROS, which is a cross-platform "social layer" that can be used on other social networks such as Facebook and MySpace. In practice, this means you don't have to leave Facebook and join Meezoog if you like the concepts I've just described; you'll be able to do it through a Facebook application.
Now, all of this sounds like a lot of fancy talk for something that won't be done very soon: having machines understand the complexity of human relationships. However, the developers behind TROS and Meezoog point out that these technologies are aimed to be used for dating purposes. I have never seriously participated in a dating social network, but I can imagine that trust is a very important thing in such a network. If Meezoog can help you better understand who you can trust - even to a moderate extent - then it's useful.