PCA is an unsupervised technique which allows the user to inspect multidimensional data through a (usually) small set of new coordinate axes (the principal components). Running PCA enables the user to:
The new coordinate system is chosen to explain as much of the variance in the data set as possible. However, we do not in general keep all the dimensions in the new coordinate system as we know that their importance is inverse proportional to their index. Late components usually only contain noise.
So the first component point in the direction of maximum variance. The second component point in an orthogonal direction to the first with maximum variance and so on. Another way of looking at the PCA process is to see it as a data compression technique. In fact PCA has been and still is used as a method for highly efficient compression of e.g. images and audio signals.