Hemorrhoid/fissure. The two most common causes of minor bleeding after defecation are hemorrhoids, which are swollen blood vessels, and a fissure, or crack in the skin lining the anus. A fissure can occur after passage of large, hard stool. Neither of these are likely to be serious. Keeping your stool soft with a high fiber diet or stool softener may help healing. If it persists, or is high volume or black see a doc.
"Hematochezia" Passing blood with a bowel movement can be due to many different problems, including minor issues like hemorrhoids, small tears at the anus (fissures), inflammatory bowel disease, or even cancer. It is best for you to go see your primary care physician. They will take a complete history, physical examination, and blood tests, and may send you to a specialist for further evaluation and treatment.