Every one of us belongs to one or more social clusters. The people we work with or the close friends we have make up these clusters. In general everyone in the cluster has strong links to every one else. Frank belongs to my cluster because I have strong links to him.
But every one of us also has weak links to other clusters. So, let's say last year I met Erik Hatcher at OSCON. Since then I have had a weak link with him (the occasional mail or weblog cross-post). Erik belongs to his own cluster of friends and work-colleagues.
The network theorists have found out that is actually the weak links that can be very important and in fact you should make sure you gather as many weak links as possible.
Why? Let's look at an example. Say I was looking for someone to invest in my soon-to-founded open source service company (it's only an example) - if I contact people in my social cluster then chances are the "news" will only travel within that cluster and so I will only be able to reach a limited audience. In order to get the "news" to travel far and wide and reach as many people as possible, I need to send that information over a weak link (so in this example, I would perhaps send Erik an email) - so that it reaches other clusters I have no stong ties to. The information uses the weak link to jump clusters!
Something else to think about is corporate marketing. If I only use the strong links (i.e. the customers I already have) then chances are they already know what I offer anyway - so the chances are slim that I will reach new markets that way. However if I find a weak link (perhaps via an affiliated company that has it's own customer base) I can reach other clusters of companies that are perhaps open to my offer.
That's one of the reasons I write weblogs - in order to form more weak links. When I wrote about Lotus Notes as a weblog tool not so far back I got lots of feedback from the Notes community. A cluster of "people" I would not have been able to reach where it not for the weak-linking of weblogs.