How do we sort things? Let me count the ways....
Modern scientific taxonomy got started with Carl Linnaeus (1707-1778). He was the man, I must say. After spending his younger years exploring the botanical biodiversity of Sweden and northern Europe, he dedicated his mature years to sitting in Uppsala and organizing the pieces of the world that came to him in the mail. Explorers went out to sea at his behest, and some of them - the ones that survived - sent him specimens of plants, animals, stones, whatever.
Linnaeus decided to organize everything. At the time the world must have seemed suddenly knowable, all things coming clear. Everything must belong to a type, and all types must fit into a hierarchical structure. (Could it be Latin grammar that gave him this idea?)
Linnaean organization especially emphasizes two things: kingdom and genus. Kingdom defines the nature of the beast. Genus names a category and allows specification to produce a binomial - a scientific name.
To start with the binomial: The scientific name of a species consists of two names, genus and species. The genus is its generic name, or category. The species is the name of a specific type of organism within that category.
Take the lion, Panthera leo. The generic category is panthers. What kind of panther? The "lion" kind. You could also have the "tiger" kind of panther, Panthera tigris, or the leopard kind of panther, Panthera pardus, which actually means "Panther panther." (The word "leopard" comes from two Greek words meaning "lion panther," so our common name for leopard means the same thing as the scientific name for lion. Haha!)
All those generic panthers belong to the cat family Felidae. So do generic little cats, in the genus Felis, "cat" in Latin. Linnaeus named our domestic cat Felis catus. Catus is another Latin word for cat. So a domestic cat is the "cat" kind of cat. Another little cat is called Felis silvestris, the kind of little cat that lives in the forest. Simple!
Now kingdoms. Linnaeus created three kingdoms - Plants, Animals, and Minerals - to encompass everything in the world. Anything missing? Minerals fell by the wayside pretty quickly, but they weren't the real problem.
The invention of the microscope suggested that microorganisms didn't fit into either Plants or Animals. In the 1860s biologists added a new kingdom, Monera, for all single-celled organisms. But all single-celled organisms aren't alike. Some are small and primitive with no nucleus, and others are large and well-organized with nuclei and membrane-bound organelles. Scientists started calling them prokaryotes and eukaryotes. In 1938 they added another kingdom, Protista, to hold single-celled eukaryotes. The prokaryotes - bacteria and cyanobacteria - stayed in Monera.
Now, fungi are really not at all similar to plants - no chlorophyll, chitin cell walls - so in the 1960s they got taken out of Plantae and put in their own kingdom Fungi. And animals, plants, and fungi are all eukaryotes, so it was kind of important to put them with single-celled eukaryotes if cell structure was going to be a category. But they were ALREADY kingdoms. We needed another level of taxonomy. So that led to the short-lived empires - Prokaryota and Eukaryota. Kingdom Monera went into Prokaryota. Eukaryota got everyone else - Animalia, Plantae, Protista, and Fungi.
But in the 1970s and 1980s, biologists started focusing on common ancestry instead of physical similarity. Microbiologists announced that prokaryotes were not all bacteria, and that some were in fact very very different - so different they deserved their own kingdom. In the 1990s they got rid of Monera and replaced it with Bacteria and Archaea. The empires were changed into domains called Prokarya and Eukarya.
And that didn't even last very long. Now there are three domains. Eukarya still contains animals, plants, fungi, and protists. But the kingdoms Bacteria and Archaea are now in domains called Bacteria and Archaea. This leaves room for more discoveries.
Do we still need kingdoms? Does the genus-species naming structure still work? Clearly many things don't fit into the Linnaean schema. Plant taxonomy is full of subspecies and subfamilies and things just called clades or tribes. Hominin (human ancestor) taxonomy got stuck with a family called Homidae - all the great apes - and several named genera, but then has had to fit lots of categories in between them for extinct taxa. (Chimpanzees are currently grouped in a tribe called ... Panini. That's funny.)
And don't even get me started on the slime molds and water molds! Poor Phytophthora, dumped by Fungi. My kingdom for a kingdom! At least they still fit in Eukarya.
One obvious problem with imposing an organizing structure on the world is that one then forces the world to conform to the structure, rather than the other way around. (It's not an animal, and it's not a mineral, so it MUST be a plant....) On the other hand, we have to be able to talk about stuff. It will be amusing to watch this process unfold over the next decades. Will Linnaeus disappear entirely?