Principal Component Analysis
NIST - Principal Component Analysis
While mostly based on examples using R, the information at the following links also provides a decent overview of Principal Components Analysis (PCA).
Tutorial: Principal Components Analysis (PCA) in R
Principal Components Analysis: A How-To Manual for R (by Emily Manki)
"Some Notes on Principal Components Analysis" by Marco Plebani
"Visualizing principal components with R and Sochi Olympic Athletes"
Analogy of PCA with varimax rotation
Football suspended in a large cardboard box. Rotate the axes of the box until they line up in a way that maximizes the information about the shape of the football (the variation explained) using the least number of axes.