Complement is an ancient component of our innate immune system that was initially discovered in the 19th century and named for its ability to complement antibody in the lysis of cells.
In the simplest of terms, complement is triggered by one of three mechanisms (Antibody Triggers the Classical Pathway; Carbohydrates Trigger the Lectin Pathway; The Alternative Pathway is triggered spontaneously.) Once triggered, a cascade of events leads to the assembly of a C3 Convertase, which breaks C3 into the soluble anaphylatoxin C3a and the insoluble C3b, which precipitates onto the surface of the cell and forms a component of additional C3 convertase, thus amplifying the reaction, and also a C5 convertase.
C5 is then digested into an additional, more powerful soluble anaphylatoxin, C5a, and the insoluble C5b, which cooperates with other components to lead to the formation of the Membrane Attack Complex (MAC) comprised of C9 molecules inserted into the plasma membrane.
The anaphylatoxins, C3a, C5a (and, to a lesser extent, C4a), function to induce contraction of the smooth muscle and then an increase in vascular permeability of the capillaries. They further increase the expression of adhesion molecules on these same vascular epithelial cells so as to recruit immune cells to the location. Finally, they promote receptor-mediated chemoattraction of leukocytes.
In summary, complement can be activated through three somewhat distinct pathways, each one converging at a C3 Convertase. Complement will lead to direct cell death via pore formation (MAC complex formation), it will recruit leukocytes to the area of infection via chemotaxis, and will facilitate phagocytosis of pathogens via complement receptor-mediated endocytosis.
As a last note, it is relevant to bring up the presence of ‘natural antibody.’ These (IgM) antibodies are made by a special group of innate (B-1a) B Cells found most prevalently in young organisms and at lower concentrations later in life. Interestingly, these antibodies are produced prior to antigen exposure and have a pre-defined array of specificities including targets such as phosphorylcholine and certain carbohydrates common on bacteria. As such, they are distinctly innate mediators of immunity and are specifically capable of fixing complement on their bacterial targets.