A planet is a celestial body, directly orbiting a star, not sufficiently massive enough to generate photons in the range of visible light, but larger than a comet or asteroid. On both ends of the mass spectrum, it is a subjective call whether a body is a planet or not.
Planets can have atmospheres ranging from thick to none, and they can have lesser bodies orbiting them as satellites. The largest satellite (Ganymede) of the largest planet (Jupiter) is bigger than the smallest planet (Mercury). Humans have photographed all the planets in the Solar System with probes.
Pluto isn't a planet, however. Some people decided it, plainly and simply, sucked too much to be a legitimate planet. Sorry Hades.
 Rocky planets
A rocky planet, also called terrestrial planet is a planet made primarily of rock and often with metallic cores. According to theories on the development of solar systems and observations of our own, this is because heavier elements stay close to the centre of the solar system, close to the star, and form planets there. Rocky planets are one of two types of planets, the other being the Gas Giants where the atmosphere composes the majority of the planet's volume, rather than just a thin skin close to the surface. Rocky planets can also be classed as dwarf planets like Pluto when they're too small to be classed as actual planets.
 Life on rocky planets
Some rocky planets, such as Earth, are capable of supporting carbon-based "life as we know it". Conditions necessary for life are generally thought to be:
- Orbit around a yellow star (like the Sun), a red giant, or a stable combination of those stars. Stars redder than the sun may also be life sustaining as may stars slightly hotter.
- Presence of water, and carbon based organic molecules. The former is believed to be fairly common while higher resolution spectroscopy equipment has started to detect fairly large organic molecules.
- Orbit within the habitable zone.
- Presence of an active core that causes volcanic and tectonic activity as well as a magnetic field to protect the surface from cosmic and solar radiation (life evolving despite this is perhaps possible but probably far more difficult).
- The size and density of the planet have to be such that the planet's gravity can hold an atmosphere, but is not too strong to crush lifeforms.
Out of all the known planets and exoplanets, Gliese 581c and Mars are the only planets (besides Earth) to even remotely meet these criteria. However, it should be noted that current methods for detecting exoplanets are biased towards finding ones that certainly aren't Earth-like. Moons of Gas giants, notably Europa may also harbour life.
We must however not limit ourselves to searching for life on Earth-like planets inside the habitable zone, as alternative scenarios, such as volcanic activity providing heat on planets or moons outside of the habitable zone (similar to "smokers" on Earth's ocean floors), silicon-based life that can survive where carbon-based life cannot, and even floating, balloon-like lifeforms living in the atmospheres of gas giants, have been theorized.
 Rocky planets throughout the universe
Recently Pluto has been removed from the list of rocky planets, because it is similar in size to several other objects that are generally not classified as planets. Indeed there is a fine line between small rocky planets, moons and large asteroids.
Few rocky exoplanets have been discovered so far, this is most likely because their small size and mass makes them difficult to detect.
Stars with planetary systems are believed to be quite common, however, and as new detection technologies are developed, more rocky planets will almost certainly be discovered.
 Gas giants
A gas giant is a large planet consisting of gases (predominantly hydrogen and helium) held together by gravitation, although many gas giants also have a solid rocky core and icy rings surrounding the equator (though aside from Saturn's impressive ring system, they tend to be rather small compared to the planet itself, which should be obvious since the image in this section doesn't show them clearly). Gas giants are one of two types of planets, the other being the rocky planets.
Gas giants are larger and more massive, but have lower densities, than rocky planets. Clearly, being gaseous they need to be more massive in order to generate sufficient gravity to hold themselves together. Jupiter, for example, has a diameter of 142,984km (12 times that of Earth) and some exoplanets are even larger than Jupiter.
Gas giants are always incapable of supporting human life partly because they lack a solid surface, and because no human being could withstand the force of their gravity.
Most exoplanets that have been discovered so far are gas giants, and also in very close orbits. This is most likely because gas giants are large and thus more easy to detect than rocky planets via their gravitational effects on their star or occlusion of its light.
 On your calendar
Saturn, uniquely among the gas giants, has been honored by having the seventh (or sixth, depending on your personal issues) day of the week named after him: Saturday.
The Romans also called their year-end "our calendar is screwed up again" party "Saturnalia".