Simple Definition:

Taxonomy is the scientific process of categorizing and classifying living organisms [plants, animals, fungi, etc.] based on their characteristics and evolutionary relationships. For example, humans belong to the animal kingdom and are classified as mammals [animals that feed their young with milk].

Very Simple Definition:

Taxonomy is a way of organizing different types of living things based on how they look and how they are related to each other. For example, dogs and cats are both animals, but they belong to two different categories.