Simply, parallax is the apparent change in position of a nearby object relative to a distant object when viewed from two widely separated points. Our eyes are separated by a certain distance. Using the distance between our eyes works for object just a few feet away. The Earth's orbit is a slight ellipse about 186,000,000 miles in diameter. What they were seeing was parallax.
Closer stars seem to move a greater distance against the starry backdrop.
The farther the star is away from our solar system, the less it seems to move. Astronomers made accurate observations of stars that seemed move the most, taking readings six months apart. This gave them a line about 186 trillion miles across. Now they needed another angle to compute the distance to the star, and they used the distance that the star seemed to shift against the background stars. One half of this distance is called the star's parallax angle.