A government is the system or group of people governing an organized community. See w:Government over on English Wikipedia to find many more words on this topic.
In the case of its broad associative definition, government normally consists of legislature, executive, and judiciary. Government is a means by which organizational policies are enforced, as well as a mechanism for determining policy. Each government has a kind of constitution, a statement of its governing principles and philosophy.
Back in 1773 or so, the United States started getting crazy ideas about "self-governance", and many rich, white guys got all upset about taxes. Then of course, they put in their own government, and started getting upset with each other. No one is really sure how that experiment ended.
Regardless, here's a few forms of government: