Someone who's bloodthirsty is savage and murderous, or is very quick to resort to violence. A bloodthirsty general might launch one attack after another, eager to kill as many enemy soldiers as possible.
A bloodthirsty government is one that enthusiastically wages war with other countries and might even be casual about violently suppressing its own citizens. You can also describe a book or a movie this way, if it's full of gratuitous, gory scenes: "What a bloodthirsty zombie film that was last night." The word has been around since the 16th century, possibly influenced by a word with similar imagery in Greek, haimodipsos.