Entertainment is one of the three outputs of Commercial Revenue, directly spending tax revenue on producing Happy Faces for the local city (rather than some national effort).
The output of happy faces is dependent on the local city's commercial output and the ratio determined nationally (by the domestic advisor) at a rate of 1 happy face for 1 commerce, so if the entertainment rate is set to 20% - 20% of the commercial output for the local city will be spent on entertainment.
Entertainer Specialists can also increase Entertainment in a city.