When you have a key, you need to be sure it belongs to the person you want to communicate with. If you've met them yourself, this is easy, you simply check the fingerprint that they gave you matches the fingerprint of the key you downloaded from a public keyserver. But if you've never met them, you'll have to rely on other people.
The OpenPGP standard allows anyone to place a certificate on a userid saying "This key belongs to this person". This is commonly referred to as "signing somebody's key". Each user can configure how many certificates a key needs in order to be trusted.
If you look at these links amongst a large group, they form a complex web of trust showing who has certified whose key as being valid. The better-connected a key is, the more likely it is that somebody will be able to trust that key.
Several people run periodic analyses of the global web of trust which rank people according to how tightly they are connected. I have a trend analysis called Footsie that shows how the Web of Trust is changing over time.