Chöd, also know as the spiritual practice "to cut through the ego", with the tradition of feeding your demons was brought into a version using Gestalt tools (embodiment of aspects and setting
them on different chairs for a little chat).
Lama Tsültrim Allione was at some point Tibetan buddhist nun and later went into therapy due to personal loss. When she then came back to the monastery she happened to get introduced to the original practice from Lama Machig Labdrön (11th century) and later decided to bring it in a simplified version to the western world.
Please note that I am not a buddhist and thereof lack more detailed background on the buddhist and Tibetan buddhist philosophy.
When we speak of demons in this context we talk about any kind of attachments and reactions that we have, that turn out in a negative way. It could be "the need to be in Facebook" or "an unstoppable desire to eat chocolate". It is a quite different concept it seems to me than the demons in the christian religion. The word demon derives from the greek daimon, which were creatures without physical bodies which were sometimes more and sometimes less in favour of humans.
The way we feed the demons (and resolve ego clinging each time a little bit) is to feed them our ego in the form of the nectar of how they will feel when they are really content. This might be very different qualities from what they want or need (which is part of our research in the process). As a result our externalised reaction to the topic transforms, dualism is resolved (at least a little) and what used to be an attachment/ problem, might even become a resource but with very different qualities (the ally).
But I do suggest you do the exercise a few times with an experienced facilitator, to make sure you get the idea how it works correctly!