The act of taking semen or other liquids, from a person's anus, then passing it on mouth to mouth.
To suck the semen, or other fluids, from a person's rectum, and to then share it, orally with others, or not. This can involve the swallowing or not of the fluids.
(In a Cultural Sense) Believed to have been conceived by the creators and cartoonists of Zap Comix in 1975.
To spread the butt cheeks, to then suck the anus, to draw the fluids into one's own mouth. Then to, either swallow it, or to pass it on to others in the room, mouth to mouth.
While close to 'rimming' it isn't the same. Rimming is more about stimulating the anus, while felching is the sucking of fluids.
Practice (Associated Acts): The licking of the anus, can be part of 'felching' but the primary act, is the sucking of fluids, (semen) from the anus.
Noteworthy: Reference to this particular act, is common in many sitcoms, such as the old All In The Family, in South Park even.