System of branching divisons that biologists use to place an organism into the appropriate taxon.

What would the word be that fits that definition?

Here are some possible words:
binomial nomenclature
classification system
homologous structure
kingdom
natural selection

I've narrowed the word to the following. I'm not quite sure which it is.

The word that fits the definition you provided is "classification system." Biologists use a classification system, often referred to as taxonomy, to place organisms into specific taxonomic groups based on their characteristics and evolutionary relationships. The classification system involves a hierarchical structure with various levels of classification, including kingdom, phylum, class, order, family, genus, and species. Organisms are grouped into these taxonomic ranks based on shared characteristics and evolutionary history. By using a classification system, biologists can organize and categorize the immense diversity of organisms found in the natural world.