From wikipedia:

dimensionality reduction or dimension reduction is the process of
reducing the number of random variables under consideration, and
can be divided into feature selection and feature extraction.

What is the difference between feature selection and feature extraction?
What is an example of dimensionality reduction in a Natural Language Processing task?

Simply put: 


feature selection: you select a subset of the original feature set; while
feature extraction: you build a new set of features from the original feature set. 


Examples of feature extraction: extraction of contours in images, extraction of digrams from a text, extraction of phonemes from recording of spoken text, etc.

Feature extraction involves a transformation of the features, which often is not reversible because some information is lost in the process of dimensionality reduction.
