In reply to Sam Watson.

> Does having less number of principal components signal that the particular data set can be classified into classes much easily?

No, not necessarily. It depends on how you are classifying and what the pre-processing step does. In general, there is no reason to think that
fewer PCs improves the classification.

> Basically what does it mean when the number of principal components are lower?

When there are k PCs, it means that most of the variation in the data occurs in k dimensions. For example, a 3D scatter plot that looks like the interior of a rugby ball has three PCs because there is lots of "thickness" in the scatter in each of the three dimensions. In contrast, a 3D scatter plot that looks like a frisbee (flying disk) has two PCs because two dimensions of the data are "thick" (the disk) whereas one dimension (the height) is thin relative to the other dimensions. So fewer PCs means that the pre-processing step is squashing or compressing some dimensions.