Image: Jupiter, the largest planet in our solar system is a gas giant. Credit: Stellarium/KRC

A planet is a spheroidal, naturally formed, body which orbits the Sun but is not a satellite and does not orbit another planet. The term planet (meaning 'wanderer' in ancient Greek) can be broken down into several sub-categories:

Terrestrial Planets, these are the 'Earth-like' inner planets of our solar system, Mercury, Venus, Earth and Mars

The Gas Giants, these giant planets consist mostly of of hydrogen and helium just like a star but do not have enough mass for nuclear fusion to occur. Jupiter, Saturn, Uranus and Neptune are considered to be gas giants.

The Ice Giants are a special type of gas giant planet. Like gas giants they consist mainly of hydrogen and helium but are also rich in ammonia and water. Uranus and Neptune are both thought of as ice giants.

Dwarf Planets - The term dwarf planet is a new type of designation formalised by the International Astronomical Union in 2006. It refers to small planets which are roughly spheroidal but which have not cleared their neighbouring region of other planetesimals (such as small asteroids and Kuiper Belt Objects). Ceres, Pluto, Makemake, Haumea and Eris are all dwarf planets.

Plutoids are dwarf planets but refer to the planet Pluto and any dwarf planet in our solar system beyond the orbit of Pluto. 

Minor Planet is a rather vague term but generally means any large object in the asteroid belt. Ceres was often referred to as a minor planet until it was redesignated as a dwarf planet.

Extrasolar Planets are planets which orbit stars outside our solar system.