Fibrinous exudate forms when there is a significant increase in vascular permeability, allowing fibrinogen to escape from the bloodstream into the affected tissue. In the presence of tissue damage or inflammation, fibrinogen is converted into fibrin through the action of thrombin. The fibrin then polymerizes to form a dense, fibrous network. This process is commonly seen in conditions such as pneumonia, pericarditis, and pleuritis.