Let's take the terms,first :prinicipal , second :component , third :analysis. Principal is kinda mathematic's way of saying something is important or critical.

Let's take the terms,first :prinicipal , second :component , third :analysis. Principal is kinda mathematic's way of saying something is important or critical. Component is basically referring to parts Analysis is basically referring to ability of this method to help you understand what's going on with your data. So the main idea here is like actually pretty simple. Let's say you want to understand what makes a difference to a person's SAT score. You track number of hours of study, maybe the average school SAT scores, age of the person, average of mock SAT scores. Now you know that some of the columns of data are more important than other and you want to know which one? So in regression what you would do is fit a line that best lies in the middle of these points by playing around weights or 'importance' of the columns till you get least distance from points. What PCA does is it tells you which variables are important and gives you a sense of ranking of these variables. So it has the ability to select variables, rank it's importance and tell you what columns of data matter more than others. Ergo it tells you which components are principal and helps you analyse them through their importance ranking. Because this method does so many things you can a do a ton of cool stuff. If you have a ton of data, this method can tell you to focus on these 3 or 4 columns which have the biggest impact. So it can help you prioritize Second if you are looking at optimizing your system,let's say SAT scores, this system can tell you a better school can make a bigger difference than just brutal hours of practice. In networks like social networks, it can tell you who is the most important/ prestigious/ coolest person by looking at friendship or social messaging links between people. So to sum up, it gives you an idea of what is important in your data, gives a sense of the quantum of its importance and hence gives a deeper feel for what's going on. One big point with PCA is that it's a linear method. Which means variables which have exponential impact on your study will not get signalled well. So transformation and processing your data is critical for this method to work. Hope this helped.