A Justice of the Peace (often abbreviated as JP) is, within the American court system, a court that is the lowest rung on the judicial ladder.
Justices of the Peace generally have jurisdiction in matters which do not involve jail time or which involve (relatively) minor amounts. A Justice may or may not be required to be an attorney, but usually must have some training in the law.
One of the more notable functions is their ability to issue marriage licenses (and to perform ceremonies for persons who do not want, or cannot timely arrange, a religious ceremony).
As an example, in Texas these courts have jurisdiction over: