The three-domain system is a method for classifying cellular life which was initially proposed by Carl Woese in 1990. While the three-domain system met with some initial opposition, it has since become widely accepted, thanks to scientific discoveries which have supported Woese's proposal. Under the three-domain system, all cellular life can be divided into three domains: Archaea, Bacteria, and Eukaryota, and each domain can be further divided into kingdoms, phyla, classes, and so forth.
This classification system distinguishes between eukaryotic organisms, organisms which have cells which include a nucleus, and two types of prokaryotic organisms, organisms with cells which lack a nucleus. Initially, Archaea and Bacteria were both lumped together as prokaryotes, although each group had its own kingdom. Woese argued that Archaea and Bacteria were so distinct that they actually belonged in separate domains, not just separate kingdoms.
The differences between Archaea and Bacteria primarily have to do with complex genetics. When Woese first published his proposal, genetic research seemed to suggest that the two kingdoms were descended from a common ancestor, and that they were similar enough that they did not require separate domains. As a result, the three-domain system was initially viewed with skepticism.
However, further research indicated that Woese was actually right, and that these organisms were so genetically distinct that they needed their own domains. Archaea and Bacteria are both prokaryotic, but their cellular structures are markedly different, and they have very distinct ribosomal RNA, indicating that these domains diverged a very long time ago, and are largely unrelated. The three-domain system for classifying organisms seems to be more accurate than previous systems now that evidence to support it has been discovered.
Within Archaea, there is only one kingdom, also called Archaea. The Bacteria domain also hosts only one kingdom, known as Bacteria. Eukaryota can be divided into four kingdoms: Animals, Plants, Fungi, and Protists. Within each domain, there is a huge diversity of life, ranging from extremophilic Archaea which thrive in environments which would kill most other life on Earth to fragile tropical orchids in the Plant kingdom.
This system is especially important to people who study prokaryotic organisms, since the three-domain system underscores the difference between Bacteria and Archaea. Researchers typically specialize in one or the other, using genetic research to learn more about the organisms they study. Some people still use the two-empire system, which divides cellular life into Prokaryota and Eukaryota, and then into respective kingdoms, but this is becoming increasingly rare.