TITLE: Intuitive Way To Understand Principal Component Analysis
QUESTION [24 upvotes]: I know that this is meant to explain variance but the description on Wikipedia stinks and it is not clear how you can explain variance using this technique
Can anyone explain it in a simple way?

REPLY [11 votes]: Spent the day learning PCA, hope my cartoon translates the intuition over to you! 
I have also tried to briefly explain the utility of PCA and related it to an analogy (no maths) to help give that feeling of "learning closure".
Visual Intuition (zoom in)

Intuition via Utility
I think the main usage for PCA is to be able to categorise different distinct "things" e.g. Shiny cells vs. Dark cells in a way that leads to least error (in terms of predicting the right colour cell). E.g. Imagine sam was hiding behind me and I pinched a cell off the left side of his body then asked you to guess the color of the cell, by looking at the winning photo, or even the winning line, you can make a very good guess it will be a "dark cell".
Intuition via Analogy
So my understanding is that PCA is like taking a "picture" in a lower dimension, but the various methods used out there attempt to make the picture as informative as possible by deciding which "angle" to take the picture from (notice for 1D the angle of "squishing line" also vary).
Good video
http://www.youtube.com/watch?v=UUxIXU_Ob6E