I like the way some of the articles below describe pure and applied research.

Pure research is “research made without any idea of application to industrial matters but solely with the view of extending our knowledge of the Laws of Nature.” So it applies to “real life” in the sense that it extends our knowledge about the universe. Pure research can also, eventually, indirectly impact the “real world” because results of pure research can then be used for applied research. Examples of pure research would be: determining the gravitational constant in the “law of universal gravitation,” developing linear algebra and calculus theories to extend our knowledge of mathematics, etc.

Where applied research “is the application of knowledge from one or more natural scientific fields [pure research] to solving practical problems.” Examples of applied research would be: using linear algebra and calculus to design and develop the computer you’re using, using the law of gravity to design a slope of a roller coaster that isn’t so steep that it kills people, etc.

NOTE: The examples are based on my understanding of the topic.