"Like" is a button on Facebook that indicates approval or interest in someone's status, picture/video or comment on the above. Clicking "Like" displays your name as a person who "Likes" this. Other than that, I am not sure what effect it has, although I suspect that Facebook has some type of algorithm where posts that get more "Likes" and comments are displayed to more people, leading to more likes and comments, and so on.
As a mechanism, "Like" isn't particularly bad, and is not particularly good. One of biggest problems with "Like" is that it can mean either approval or interest. Since "Liking" something on Facebook is a polite thing to do to items of interest or import, I sometimes see people liking statuses such as
"My grandfather is in the hospital with pneumonia. It looks serious."
It is for this reason that
Google Plus has called its similar mechanism "+1", which merely states that an item is of interest, without the approval of "Like".
The other problem of the "Like" button is that it is a way to enter a conversation without saying anything. In general, conversations on Facebook are superficial and transitory, and the "Like" button doesn't add to dialogue. I have found myself wanting to reply with "Like" in other places instead of coming up with an actual response. It is somewhat akin to the infamous "me too" of the AOL era.
However, not much should be read into the "Like" button, although I have to admit that when a photo or post of mine crosses the 10 like threshold, I become proud.