A question, alas, with no simple, well-agreed-upon answer, but I'll do my best to explain what I have observed people to consider it.
ASFR deals with a sexual fascination with the idea of controlling or immobilizing another person. Among the ideas that you might expect to find in a story labelled "ASFR" are:
ASFR is not a group, club, organization, or movement. Nothing about it is "official;" there is nothing to "join," there are no "requirements" of membership. It's just something a bunch of people like, and you might like it too.
Many, though not all, stories labelled ASFR deal with these ideas in a sensual or sexual way. Many include nudity. Many include sex. Some include graphically described sex.
Although many people disagree, I think ASFR could be considered somewhat related to bondage, in that it generally involves some participants dominating others. Our preferred methods of domination are different and mostly impossible in the real world without a healthy dose of imagination.
ASFR stories aren't always nice - people are sometimes kidnapped and immobilized, transformed into something non-living, or forced into obedience. On the other hand, some ASFR stories are quite romantic, exciting, fun, or even funny.
It's because of this wide variation in what is called ASFR that this site exists. I'm trying to provide an opportunity for ASFR lovers of various different tastes to offer their own personal favorites of the genre - and without a doubt, there will be a wide range of tastes represented here. Perhaps in the process, this site will ultimately provide a better "definition" of ASFR than any one person could.
It is not the goal of this site to push ASFR on anyone who isn't interested in it. If it doesn't appeal to you, please enjoy the rest of the web. But if you'd like to see what it is we like... at the risk of maybe discovering you like it too... then stick around and look at some of our favorite stories.
It may be important to mention that ASFR fans do not actually try to transform people into objects, control them magically, or treat them like robots (except perhaps in consensual roleplaying situations). Most of us wouldn't if we could. Enjoying ASFR is no more inherently immoral than, say enjoying a murder mystery or war movie - you can enjoy reading or fantasizing about it without wanting to emulate it.
By the way... if you were wondering, the acronym "ASFR" originally came from a newsgroup, alt.sex.fetish.robots. It's mostly filled with spam these days, but if you look for posts with "ASFR" in the subject line, you might find some interesting traffic.