Opposition is the astronomical state of a planet (or other body) being directly opposite the sun as seen from the earth. Only the superior planets (Mars, Jupiter, Saturn, Uranus and Neptune) can reach opposition. In addition, the moon, as a satellite, goes into opposition, but at such times it is usually referred to by the more colloquial "full moon".
From the viewpoint of the Earth, a planet reaches opposition about once a year, plus the time that it takes the earth to catch up with the planet's motion. This is something that is hard to explain in words, but is rather simple in a diagram. For instance, Saturn moves very slowly across the sky, so by the time the Earth has returned to its former position in orbit, it has almost caught up with Saturn, and opposition occurs in about the same place. On the other hand, with Mars, by the time that the Earth has caught up with the position where Mars had been in opposition the previous year, Mars has already moved on, and thus the time between Mars' oppositions is greater than that between Saturn's oppositions.
Opposition is also, ceterus paribus, the time when a planet is at its brightest. There are other factors with this, such as whether the planet is at or close to aphelion, or (in the case of Saturn), whether it is presenting its rings towards the Earth. A planet at opposition, being 180 degrees away from the sun, will also rise at sunset and thus will be free for viewing throughout the night.