Feederism is considered a fetish or paraphilia.
Feeders derive sexual pleasure from feeding their partners (often to the point of extreme obesity).
Gainers derive sexual pleasure from eating (and typically becoming as large as possible).
However, most feeders are not in relationships with gainers, who are rare - they're typically in relationships with obese partners who gain weight to sexually satisfy their feeder partners. These partners are called feedees. For the sake of simplicity, I will refer to feedees as the partners of feeders, even though some are clearly gainers.
There's an ongoing debate about the nature and health of feeder/feedee relationships.
Fans of feederism typically claim that feeder/feedee relationships are fully consensual, that power is shared equally between the partners, that both the feeders and the feedees derive sexual pleasure from the feeder/feedee dynamic, and that the couples are fulfilled by their relationships. This is likely true for some, if not many, feeder/feedee relationships (although there isn't any good research, so we don't know).
On the other hand, critics argue that feeder/feedee relationships are highly exploitative and manipulative, and are extremely dangerous for the feedees. Critics claim that the feeders are predatory, taking advantage of women with extreme low self-esteem and poor body image.
Fat Girls and Feeders is the documentary that explores the feeder/feedee relationship. It paints a very pathological picture.
You can download it here (NSFW and not for the faint of heart).
On YouTube:
Not long after the documentary was released, Gina, the woman featured in it, had these scathing words to say in defence of her relationship: link here.
There are websites devoted to the feeder scene. These two appear to be the largest: links here and here.
For a critique of feederism, click here.
There's a defence of feederism in the reply section, submitted by someone who is not part of the class but who came across the post last year.
Another mini-doc about feederism from Vice: