A bacterium is a living cell consisting of a fluid called cytoplasm enclosed by a cell membrane and cell wall. A bacterium contains DNA in the cytoplasm in the form of a chromosome. Although a bacterium only has one chromosome it can have other, smaller DNA elements called plasmids. The chromosome of a bacterium is never surrounded by a nuclear membrane and this fact defines a bacterium as a prokaryote. Organisms that have their DNA in a nucleus surrounded by a nuclear membrane are called eukaryotes. A bacterium also has ribosomes in the cytoplasm. Ribosomes are involved in making proteins.
Many people confuse a bacterium and a virus. They are totally different in many ways. A bacterium is much bigger than a virus. A bacterium is much more complex. One very important difference is that a bacterium can be killed with an antibiotic while a virus cannot. So if you have a viral infection antibiotics will not help. However, antibiotics are sometimes used to prevent people with a virus infection from catching another (bacterial) infection.
Viruses and bacteria are both microorganisms. The study of bacteria is called bacteriology and it is a branch of microbiology.