How exactly dependent variable is expressed in terms of independent variables using Partial Least Square Regression Method?
This lecture helped me get my head around PCA: https://www.youtube.com/watch?v=a9jdQGybYmE

The analogy that I am sharing with you comes directly from this lecture:

Imagine that you have a weight that is on a spring. It can bounce up and down and thus is a one degree of freedom system. Imagine that you have three sensors which record the (x,y) position of the weight as it bounces up and down. Now you have six vectors of data (a set of x,y from each camera). PCA tries to infer the actual (x,y) coordinates of the weight as it bounces based only on the data that you get from the cameras.

This analogy is very rough and I highly recommend that you watch the linked video. There is really no short answer to your question!