Hemorrhoids
There is no precise definition of hemorrhoids but here are a few for starters:

“What are hemorrhoids? A precise definition of hemorrhoids does not exist, but they can be described as masses or clumps (”cushions”) of tissue within the anal canal that contain blood vessels and the surrounding, supporting tissue made up of muscle and elastic fibers.” Medicine Net, Inc.

“Hemorrhoids (AmE), haemorrhoids (BrE), emerods, or piles are swelling and inflammation of veins in the rectum and anus. The anatomical term “hemorrhoids” technically refers to “‘Cushions of tissue filled with blood vessels at the junction of the rectum and the anus.”[1] However, the term is popularly used to refer to varicosities of the hemorrhoid tissue.” (Ref. [1] MedlinePlus Medical Encyclopedia). Wikipedia

“What are hemorrhoids? The term hemorrhoids refers to a condition in which the veins around the anus or lower rectum are swollen and inflamed. Hemorrhoids may result from straining to move stool. Other contributing factors include pregnancy, aging, chronic constipation or diarrhea, and anal intercourse. Hemorrhoids are either inside the anus—internal—or under the skin around the anus—external.” National Digestive Diseases Clearing House (NDDIC)

If you suffer from them like around 50% percent of the American population by age 50 then you already have a grasp of the discomfort they can cause.

As they say a picture speaks a thousand words, source is Wikipedia:

Diagram to show a variety of Hemorrhoids. Drawn by User:WikipedianProlific

 The right hand side shows the hemorrhoid cushions in their normal state. The upper “internal cushions” and the lower “perianal blood vessels”.

The left hand side shows the internal hemorrhoid cushions, now enlarged internal hemorrhoids as prolapsed hemorrhoids. This is the term for when they swell up and extend through the anus.

The left side also shows enlarged external hemorrhoids.

Hemorrhoid symptoms

Hemorrhoids usually are not dangerous or life threatening. In most cases, hemorrhoid symptoms will go away within a few days. Although many people have hemorrhoids, not all experience symptoms. The most common symptom of internal hemorrhoids is bright red blood covering the stool, on toilet paper, or in the toilet bowl.

However, an internal hemorrhoid may protrude through the anus outside the body, becoming irritated and painful. This is known as a prolapsed hemorrhoid (or protruding hemorrhoid). Symptoms of external hemorrhoids may include painful swelling or a hard lump around the anus that results when a blood clot forms. This condition is known as a thrombosed external hemorrhoid.

In addition, excessive straining, rubbing, or cleaning around the anus may cause irritation with bleeding and/or itching, which may produce a vicious cycle of symptoms. Draining mucus may also cause itching.