The term A.S.F.R stands for Alt Sex Fetish Robot, and comes directly from a very old (now defunct) newsgroup that was dedicated to the discussion of sex with and/or sexual attraction to robots and other mechanical or robot like beings.
ASFR has come to be synonymous with the fetish itself. The fetish is really a whole area of fetish interest, activity, and behavior. For some people it is about a sexual attraction to a robot (usually one that looks and acts like a human). For many it’s an interest in the intersection of human and robot, and lots of fetishists create images which merge real people with mechanics and circuitry.
ASFR also encompasses an interest in and attraction to statues, human mannequins, life-size dolls, hypnosis and mesmerism, and “freezing” where a person is unable to move at all and frozen in place.
Fembot Central is a wonderfully friendly and supportive community forum that includes lots of discussion of ASFR.