The Bacteria Kingdom, formerly called monera, are single celled prokaryotic organisms. Bacteria encompass two domains: eubacteria and archaea. Eubacteria and archaea have very different cell walls. They are also distinguished by their DNA - the DNA of archaea has histone proteins while that of eubacteria does not.
Under traditional classification schemes Monera is the name of the Kingdom of Bacteria but in most modern textbooks, scientists due to the big diversity in the group that we normally call bacteria because there are such diversity, scientists are starting to split that into two other groups called Domains. One of these Domains is called Eubacteria, the other Domain is called Archea. So what are some of the characteristics of the Eubacteria or "true bacteria" well they're all prokaryotic which you should know what that means? They have cell walls made of a mesh between polysaccharides and amino acids called peptidioglycan.
They have what is called naked DNA what does that mean, just means it doesn't have the histone proteins that Eurkaryotic DNA like ours is wrapped around to help organize it. They have what I sometimes call "prokaryotic-style" ribosomes which if you really want to look at the details of, go ahead and Google it but most of the time you don't need to know that. And what are some examples of it, this is a huge group with huge diversity within it, it includes the photosynthetic cyanobacteria that are a major source of oxygen and food in many ecosystems. There is the nitrogen-fixing bacteria that are in our soil that help provide materials for our plants. There's lots of different kinds of Eubacteria.
The Domain Archea is a little bit unusual, now they're all prokaryotic however they have unusual cell walls made out of not peptidioglycogen but these weird other polysaccharides, even their cell membranes have unusual phospholipids within them. They don't have naked DNA like majority of the prokaryots do instead they have histone proteins wrapped around their DNA. They have "Eukaryotic-style" ribosomes, these two factors are one of the major reasons why scientists now think that ultimately the eukaryotes like ourselves and plants ultimately evolve from the Archea. Now they also have a number of different roles in the environment, many of them are Methanogens which means they're the things that in your large intestine and especially in the large intestine of things like cows. They're the things breaking down some of the undigested polysaccharides to produce methane. Halogens they inhabit really weird unusual environment and the Halogens they love salty water because by living in that kind of environment they're able to avoid competition from a lot of the other creatures. So usually they get lumped together into this group called extremophiles which simply means they love the extreme environments, and those are the bacteria.