The study of antibodies found within blood serum, to help identify disease, infections, and viruses.
The scientific study of blood serum, in that it is primarily a diagnostic tool, to determine if a person has been infected with a disease.
It can mean that a person 'was' infected, or 'is' infected, requiring further testing to make that determination more concrete.
However, it can also be used by examining other fluids, such as Semen and Saliva, which has similar properties to blood serum.
It depends on the disease being tracked, or searched for.
Noteworthy: The body stores information, on what diseases have infected it, and which antibodies it used to defend itself with. These are stored, for future references, to provide quicker response time by the body's immune system.
It is this information that serology attempts to uncover, through various tests. Generally it requires some suspicion of what to look for, in order to tailor the tests to seek that information.
Forensics can use this type of testing in the cases relating to possible rape, by sampling the serum in found semen, to that of the potential suspect.