Parallax is an optical phenomenon when the apparent position of an an object changes with the position of the observer.
In order to experience this, you can hold the your index finger some distance from your right eye - or left eye, depending on your convenience - and then moving your head slowly to the left or right, while focusing on the finger against the background.
You may notice that your finger goes to the left when the head moves to the right and vice versa. This is parallax.
The phenomenon can be used to find the distance to a far away star. In this case, the finger represents the star and the background, of course, is space.
Since the parallax angle measured will be so small if we choose two points on the Earth, even if they are poles apart, physicist have decided to use the orbit of the Earth around the Sun for the difficult measurement.
In order to achieve that, they choose two points on the orbit that are diametrically opposite - with 1 AU apart: the apparent position of the star is noted in a certain month, say January, and then after six months its apparent position is measured again; with these two measures, the parallax angle can easily be calculated; if the parallax angel is known, the distance can be easily calculated.
From the above animation, it is obvious that the distance to the star in question is reciprocal of the parallax angle.
d = 1 / ρ, where d and ρ are distance and the parallax angle respectively.
The units of d and ρ are pc and arcsecond respectively.
E.g.
If the parallax angle is 2 arcsecond, the distance will be 2pc. If the parallax angle is 3pc, the distance will be 3pc.
1pc = 3.26 light years
1 arcsecond = (1/3600)0
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