The parallax method is a way of measuring distances of far-away objects. Astronomers use parallax to measure the distance to stars.
Parallax is a measurement of the shift of a nearby object compared to distant objects when observed from two different positions.
You can see this effect for yourself. Cover your right eye and look directly at something some distance away, like a tree or house. Hold your hand at arms' length and stick up one finger, and cover the tree with your finger.
Now uncover your right eye and cover the left eye, WITHOUT moving your hand. Your finger is no longer covering the tree. The "parallax shift", the distance that your finger appeared to move (relative to the tree in the background) can be used to measure how far away things are.
For nearby objects in the solar system - for example, a comet or an asteroid - two observatories can observe the same object at the same time, and measure the "parallax angle" between the comet and a distant star. Knowing how far apart the two observatories are will let you calculate the distance to the comet.
For other "nearby" stars, we assume that the stars themselves aren't moving quickly. Take one measurement today, and another measurement exactly six months later. We know the distance between the two observations is 184 million miles (twice the Earth's orbital radius). If our reference star is far enough away, we can use the parallax angle to calculate the nearby star's distance.
For VERY distant objects, this doesn't work, for two reasons.
1. The parallax angle is too tiny to be measured accurately
2. We cannot be sure that the reference star in the background is far enough away from the "nearby" star to accurately calculate the distance.