Sildenafil (also known as the brand name Viagra) is an erectile dysfunction (ED) agent that was originally designated as a blood pressure medication indicated for pulmonary arterial hypertension, or high blood pressure within the arteries sending blood away from the heart and towards the lungs for oxygenation. The medication's mechanism of action explains how it gained popularity as a treatment for ED.
When sildenafil enters the bloodstream, it increases the systemic effects of the nitric oxide present within the circulatory system, which then activates a specific enzyme responsible for increasing levels of a nucleotide called cyclic guanosine monophosphate (cGMP). cGMP, then, does two things. First, cGMP causes the pulmonary artery to dilate which reduces the workload on the heart and increases blood flow to the lungs, thereby relieving the high blood pressure. The second thing it does is exert its effects elsewhere. cGMP causes the corpus cavernosum (the spongy erectile issue of the male appendage) to relax, promoting an increase of blood flow to said tissue which then causes erection. Lastly, the sildenafil also inhibits of the cGMP-antagonizing enzyme called phosphodiesterase type 5 (PDE5).
In short, sildenafil causes a chemical cascade to occur which increases blood flow to both the lungs and the erectile tissue of the male appendage, causing an erection and relieving pulmonary arterial hypertension, while also stopping the production of the enzyme that can inactivate the cascade's catalyst.