Parallax is a term used by astronomers to refer to the apparent change of an object's position in the night sky. It is usually used in reference to stars and planets, and can be used to calculate the distance to that object. Of course, it's not so much that the object in the sky is changing as is our position here on the Earth, as the Earth revolves around the sun.
Here's an example; let's say its the firs day of summer, and you look up in the night sky and see a star. You plot the position of the star as it appears at that particular day. Six months later, on the first day of winter, you go out looking for the same star, only to find it has changed positions in the sky. You chart the star's position at that particular day. If you were to construct a model of the sun, the Earth and the relative positioning of the Earth at the beginnings of summer and winter, you could draw a line form both days to the apparent position of the star. Where the lines intersect would be the exact position of the star. From there, it's all math; we know the distance from Earth to the sun, you would simply calculate the other lines drawn up in the model.