An extrasolar planet is any planet which does not orbit the Sun. Methods with which they can be detected include direct detection, astrometry, pulsar timing, transits and the doppler method. Although the doppler method has had most success so far transits are more promising in the long run, especially if the goal is to detect terrestrial planets. Properties of planets detected tend to these categories: Hot Jupiters (giant planets in extremely close orbits about their parent stars with low eccentricities), Eccentric Giants (giant gaseous planets in more distant orbits with high eccentricities). Pulsar Planets (any planet found orbiting a pulsar), and more familiar giants resembling the ones found in the solar system. Although no earthlike planets have been detected so far projects such as SIM, Kepler and Darwin offer hope that this will change in the future.
I will note that as of today the Extrasolar Planet Encyclopedia lists 200 candidate planets detected outside our solar system.