The immune system of vertebrates, and by definition that of humans, is organised into two main sections or "arms" (i.e the adaptive immune system and the innate or "natural" immune system) according to how they see and fight infectious organisms.
The adaptive immune system differentiates between intruders and also between the components that make them up (i.e. antigens) and is able to remember each one of them individually. This ability to remember (i.e. memory) allows the adaptive immune system to increase the magnitude and specificity of its response every time it encounters the same intruder. This is the branch of the immune system responsible for conferring protection against specific diseases following vaccination.
The cells (e.g. T and B lymphocytes) and soluble molecules (e.g. antibodies) that make up the adaptive immune system elicit two different types of immunity i.e. humoral and cell immunity. Humoral immunity, mediated primarily by antibodies produced by B lymphocytes, targets small sections (i.e. epitopes) of antigens found on the outside surface of cells. Cellular immunity, mediated by cytotoxic T lymphocytes (CTLs) and helper T lymphocytes (HTLs), targets only epitopes that are presented on the surface of the body's own cells in association with HLA (Human Leukocyte Antigen) molecules .
In contrast, the innate immune system is made up of cells (e.g. phagocytes) and soluble molecules (e.g. complement) which provide a rapid non-specific protection against intruders. In other words, it detects and reacts against intruders, but it cannot differentiate between different types of intruders (e.g. bacteria, viruses, etc). As a result, the innate immune system cannot remember a specific intruder and hence will always deal with intruders in the same way, independently of how many times it encounters them.
Despite these different levels of organisation, all the components of the immune system operate within an integrated network, each communicating and supporting the others. At the centre of this network, lay the T lymphocytes and in particular the interaction between them and the antigen presenting cells (APCs). This interaction allows the immune system to differentiate between self and foreign by eliminating all T cells capable of reacting against the body's own cells. Failure to differentiate between self and foreign results in the rise of autoimmune diseases (e.g. arthritis).