Each group within a phylogenetic biological classification is called a taxon (plural taxa).
Taxonomy is the study of taxa (groups) and their position in a hierarchal order, where they are known as taxonomic ranks.
A domain is the highest taxonomic rank, and can be further subdivided into : Bacteria, Archaea and Eukarya.
Bacteria are a group of single-celled prokaryotes with the following features: lack of membrane-bound organelles, unicellular, 70s ribosomes, murein cell walls and a single DNA loop without histones.
Archaea are a group of single-celled prokaryotes, however they differ from bacteria in numerous ways. For example, their genes and proteinsynthesis are more similar to eukaryotes than prokaryotes.
Archaea membranes contain fattyacid chains connected to glycerol by ether linkages (instead of ester bonds).
The cell walls of archaea contain no murein, and they possess a more complex form of RNApolymerase.
Eukarya are a group of organisms that are made up of one or more eukaryotic cells. One of the features that they possess are membrane-bound organelles, and their membranes contain fattyacid chains connected to glycerol via ester linkages.
Eukarya don't all contain cell walls, but when they do they contain no murein.
Eukarya contain 80s ribosomes rather than 70s (bacteria). 80s ribosomes are larger than 70s ribosomes.
The Eukarya domain is divided into four kingdoms: Protocista, Fungi, Plantae and Animalia. Each kingdom consists of phyla, and diversity within phyla allows them to be further divided into classes.
Classes can be further divided into orders of organisms, and then further into families, then genera, then species.
Organisms with different domains have obvious differences in characteristics, whilst different species have less obvious differences (they are more similar).