Well sometimes dimension reduction is used to maintain the most important aspects of the data in as few vectors as possible, particularly when we want to visualize high-dimensional data or escape the curse of dimensionality. Other times dimension reduction is more of a regularization technique. Think of self-organizing maps, RBMs, autoencoders, and other neural nets that learn a representation of the data, which can then be passed to another neural net as the new training sample.

So dimension reduction is itself a technique with many distinct applications.