Parallax is the apparent displacement of a foreground object with
respect to a background object caused by the movement of the observer.
In plain words, nearby objects seem to shift more than distant objects
when you move.
Consider the following image:
In the image, there are two sets of skyscrapers, and a tall mountain
in the distance. An observer views the scene from 5 different positions.
Suppose you were to draw the scene as seen by each observing position
in the image.
Which building will appear to move the most?
What do you think would happen to the apparent position of the
mountain in the distance?
We do the same thing in astronomy to find out how far the
stars are from the Earth.
In astronomy, we can't move any closer to the stars, but we do move from side
to side. Not only does the Earth turn on it's axis every day, but the
Earth itself moves around the sun once a year.
In practice, astronomers take year round measurements of the sky
as a whole. Most stars do not appear to move (like the mountain in the
above example) but a few nearby ones seem to shift. If the exposures
from each night are laid over each other, the nearby stars will
show up as a streak across the sky. The closer the star, the larger
the streak. The streak, or parallax, is measured as angle across
the sky in arc seconds.
For a baseline given by the revolution of the Earth around the
Sun, the distance of a star is inversely related to the parallax of
the star relative to the background sky.
A special unit of distance, called the parsec, is used to make
calculating distances very easy. A parsec is the distance away something
would have to be to have a parallax of 1 arc second. This makes
the equation to find distance
D (pc) = --------
1 parsec is 3.3 light years, or about 30,000,000,000,000 km (3e13 km).