Eubacteria are one of the two major groups of single cell organisms that lack nuclei and many other organelles found in eukaryotes. They have vast diversity, with a wide range of habitats and lifestyles, but all either have an elongated helical shape, a rod shape or a sphere shape.
Eubacteria all have cell walls made of peptidoglycan, a different substance than the cellulose found in plant cell walls. Not all have flagella for moving around, but those that do are quite different from those found in eukaryotes, and are made from a single large protein filament. Their DNA is also often found in just one chromosome, which can be quite large. Bacteria reproduce by binary fission, which is a much simpler process than the mitosis by which eukaryotic cells divide.
Eubacteria fit differently into different taxonomic naming schemes. The group is often referred to as a kingdom, but it is also thought of as a division, which is the level above kingdom and usually contains several kingdoms of life. This is because of how radically different from other major divisions of life eubacteria are. They have major differences even with the other division of cells that lack nuclei, the Archaea.