As far as practical applications are concerned :
Here are a few:
1) Aircraft Engine Anomaly Detection: Input Features can be heat generated by engine, vibrational intensity, fuel consumed etc etc. Here outliers can be sent for testing again and further decisions can be made.
2) Fraud Detection : Features can be features of users activities on a website. We can model probabilities from the data. Identify unusual behavior by checking probability less than certain fixed threshold.
3) Monitoring Computers in a data center : features can be memory use, no of disk accesses, CPU load, network traffic etc. Abnormal behavior here can help predict future breakdowns.
Anomaly Detection is done assuming our data has a probability distribution(gaussian). We can plot data to see if thats the case, if not we can make it gaussian using log transforms. Gaussian distribution specifies the regions and probabilities of our data lying in those regions.
For example : replace original feature x -> Log(x) or feature x -> (x)^4/3 etc..
Also regarding the threshold value which decides outliers you can play with it and see that with Higher threshold you will be rejecting more entries and this might be required where doctors are trying to isolate cancer patients amongst many normal ones without taking any risk/chances. Again outliers here doesn't mean cancer patient but definitely worth a medical test. And you can set it to lower value if you are getting too many normal data flagged as outliers.
We have skewed data sets since we have more examples of one kind than the other. For example when we get air craft engine data we might just have data for few bad ones and mostly for good ones.Use of cross validation data is suggested.F1-Score is a pretty good metric to evaluate the performance of the algorithm.