Taxonomy is the branch of biological science which includes nomenclature and classification of the organisms into groups based on their shared features and characteristics.
Classification is the process of grouping organisms based on observable features in to categories called 'taxa'. This process involves hierarchy of steps where each taxa represents a rank. All the steps/taxon collectively is referred as taxonomic hierarchy. The ranks/taxa have the following sequence from largest to the smallest with similarities in organisms increasing at each step. Kingdom, phylum, class, order, family, genus and species form the hierarchy in classification where Kingdom is the largest rank and species is the lowest with maximum similarities.