Taxonomy is the science of classification and grouping of concepts and objects. In WordPress, it’s a type of grouping used to collect content into terms. A site can, for instance, group posts into categories like “Product updates” and “Press releases”. In that case, “Category” is the taxonomy and “Press release” is a term within the taxonomy.
WordPress includes two user-facing taxonomies out of the box: categories and tags. Both are used to group posts. Additional taxonomies can be added by themes and plugins. For example, if you’re running a recipe site, you probably have a custom post type called “Recipe” that contains all of your recipes. In that case, you could add a taxonomy called “Ingredients” to the recipe post type, and make it possible for visitors to sort recipes based on which ingredients they contain.