A Transit of Venus is the movement of Venus directly across the face of the Sun, as viewed by someone on Earth. Think of it as similar to a solar eclipse, except that the angular size of Venus is way too small.
A Transit of Venus is a rare event. It occurs in pairs, separated by 8 years, followed by a wait of either 105.5 or 121.5 years. The best that most anyone can hope for is to experience two of them.
A Transit of Venus can be used to determine the average distance between the Sun and the Earth (known as the astronomical unit, or AU). The great Sir Edmond Halley (of Halley's Comet fame) was the first to champion doing this. Knowing the AU is important, because all of the orbital radii of the planets can be determined from this one number using Kepler's Third Law.
In modern times, measuring the AU has been done by bouncing radar off Venus when it is at maximum elongation.
Click on the video below to watch the last Transit of Venus from 2004.