Dimensionality reduction is the process of reducing the number of features in a dataset. This is important mainly in the case when you want to reduce variance in your model (overfitting).
Wikipedia states four advantages of dimensionality reduction (see here):
It reduces the time and storage space required
Removal of multi-collinearity improves the interpretation of the parameters of the machine learning model
It becomes easier to visualize the data when reduced to very low dimensions such as 2D or 3D
It avoids the curse of dimensionality