IIRC Google tried something along these lines. You could (maybe still can?) sort of meta moderate search results letting Google know which ones you thought where 'best'. Same thing here, by liking a page you lend relevance to that page.
I believe OneRiot also does something like this. They have a widely installed toolbar that is out there collecting information about what users are looking at. It aggregates this information to figure out what is important at this particular moment. In other words, it determines relevance by attention. Facebook would be doing something similar here. The more attention (likes) a page receives, the more relevant it is.
I'm not sure if that actually delivers better results, or even meaningful ones at all. It's definitely an interesting move tho.