As an older user of Facebook, it drives me crazy when I "like" something that is tragic. I "like" the report of the hurricane damage, etc. Wish there were some other term! However it is so well established that I guess it is the one that has to be used. 

Basically when I "like" something in Facebook, I am saying I agree with the sentiment or your opinion, or I read the linked article and it was spot on, or hey, I loved this picture of your dog.