Feature selection vs Feature extraction. Which to use when?
Adding to The answer given by Toros,

These(see below bullets) three are quite similar but with a subtle differences-:(concise and easy to remember)


feature extraction and feature engineering: transformation of raw data into features suitable for modeling;
feature transformation: transformation of data to improve the accuracy of the algorithm;
feature selection: removing unnecessary features.


Just to add an Example of the same,


  Feature Extraction and Engineering(we can extract something from them)



Texts(ngrams, word2vec, tf-idf etc)
Images(CNN'S, texts, q&amp;a)
Geospatial data(lat, long etc)
Date and time(day, month, week, year, rolling based)
Time series, web, etc
Dimensional Reduction Techniques (PCA, SVD, Eigen-Faces etc)
Maybe we can use Clustering as well (DBSCAN etc)
.....(And Many Others)



  Feature transformations(transforming them to make sense)



Normalization and changing distribution(Scaling)
Interactions
Filling in the missing values(median filling etc)
.....(And Many Others)



  Feature selection(building your model on these selected features)



Statistical approaches
Selection by modeling
Grid search 
Cross Validation
.....(And Many Others)


Hope this helps...

Do look at the links shared by others.
They are Quite Nice...