Islam makes a sharp distinction between Muslims on the one side and everyone else on the other. Their laws distinguish this too. In Shari'a law, a Muslim can testify in court against a kafir, but a kafir may not testify against a Muslim. In Shari'a law, it is illegal for a Muslim to kill a fellow Muslim, but it is not illegal for a Muslim to kill a kafir. A kafir is an unbeliever, an infidel.
Political Islam has a good definition also: Defining Kafir, complete with quotes from the Koran describing how Muslims ought to deal with kafirs. It's not pretty.
Answers.com defines it this way:
Kafir is an Arabic word literally meaning "ingrate." In the Islamic doctrinal sense the term refers to a person who does not recognize Allah or the finality of the prophethood of Muhammad and hides, denies, or covers the truth. In cultural terms, it is a derogatory term used to describe an unbeliever or an apostate from Islam. It is usually translated into English as "infidel" or "unbeliever."
The word kāfir is the active participle of the root K-F-R "to cover". As a pre-Islamic term it described farmers burying seeds in the ground, covering them with soil while planting. Thus, the word kāfir implies the meaning "a person who hides or covers". In Islamic parlance, a kāfir is a word used to describe a person who rejects Islamic faith, i.e. "hides or covers [viz., the truth]".