10,000 likes? What does the word "like" mean here?

in this case "likes" means support or acceptance of something, on facebook if you support a cause or are a fan of something or someone you click a "like" button on the facebook page to show your support

At the social networking web site Facebook, if there is a page of which you approve, you are given the opportunity to click on a link entitled "like." So, for example, if i visited your page at Facebook about obscure almost incomprehensible medical journals, and was charmed by it, i might select "like." Then anyone who is on my friends list would see a message which reads "Setanta likes this page." Everyone who visited your page would see a message which would say that "X people like this page," where X would be the number of people who had clicked on the "like" link.

This author was asking people to predict who long it would take for ten thousand Facebook members to click on the "like" link for a specified page.

i liked your post...

I'm going to unfriend you for that . . .

oh yeah?
then i'll just go ahead and follow you on twitter...

Thank you guys.
Behind our corrupt government's firewall, I couldn't visit facebook.
But I will try out my wall-climbing software.

ok, but please wear a helmet and some knee pads...

It's a vote. It's a way of tallying positive votes.

(There's no way of tallying negative votes on the Facebook system, which would be a "dislike".)