A blood culture takes blood from the patient and places small quantities of it in a sterile mixture of blood and an agar gelatine. As the patient's blood will not replicate in such conditions, if there are any bacteria or fungi in the blood, they will grow in colonies in the agar which will be visible to the naked eye. Those bacteria and fungi can then be viewed under a microscope to identify them. As such, blood cultures can provide a definitive diagnosis for many forms of infectious diseases.
However, blood cultures do have their drawbacks. The culture must be incubated at the appropriate temperature (98.6 F, 37 C) for at least 24 hours to provide results. As most of the bacteria will respond to a normal course of antibiotics, modern medical practice is to treat any patient suspected of having an infection rather than wait for the results of blood cultures. As such, they are often used when the patient has a fever and does not respond to antibiotics.
In addition, some bacteria will not grow in a blood culture ("culture negative") and, as such, a negative blood culture cannot definitively rule out a bacterial infection. Viruses will not grow in culture at all.
The technology is an old one, dating back to the middle of the 19th century and the first work on bacterial agents. Robert Koch did most of his groundbreaking work with blood cultures. It was a ruined blood culture in the lab of Alexander Fleming that led to the discovery of penicillin.