Applied science is about using the findings of science to do something. In the natural sciences, this is done by engineering. In sciences such as psychology, this can mean using theoretical findings to improve a test method, for example.
Applied research is generally done to solve a problem. Applied chemists invented refrigerants long ago to cool things. Some refigerants escape into the atmosphere and damage the ozone layer, so chemists have developed new refrigerants in another example of applied research. This work not driven by a desire to know, but by a desire to solve a specific problem.