Small tears or splits in the lining of the anus (anal mucosa) near the anal opening are known as anal fissures.
They are usually harmless complication of difficult bowel movements.
Straining to pass a stool, having constipation and passing a hard, dry stool, chronic diarrhea are the most common causes for these tears to appear.
Rough or excessive wiping of the anus after passing a motion, inflammation of the anus and rectum due to inflammatory bowel disease are additional causes.
Rarely, they may indicate presence of rectal/anal cancer.
Anal fissures tend to heal on their own within a couple of weeks, but, if the underlying cause isn't solved (like constipation), they'll tend to reappear.
Because they are usually associated with severe pain during defecation and afterwards, anal muscles are contracting leading to decreased blood flow in this area, resulting in incomplete healing or chronic fissures.
Try soaking in a shallow tub of warm water (sitz bath) 2 or 3 times a day, increase fiber in diet, drink plenty of water, and use a nonprescription ointment such as zinc oxide, Preparation H, Anusol, or 1% hydrocortisone to soothe anal tissues.
Practice anal cleaning with water and soap after every defecation to avoid infection of the injured area.

If home treatments aren't helpful and tears reappear again, see your physician (surgery is an option for recurrent tears).

Best wishes!
Marija