Short and long loop feedback generally refers to the hypothalamic-pituitary system of hormones.
This system relies on a small cascade. First, the hypothalamus recognizes something in the body that must be corrected, so it releases a hormone that will travel to the pituitary gland. The pituitary gland then releases a separate hormone that will travel throughout the body and activate a certain set of endocrine glands. These glands then secrete a hormone which performs the desired function.
When discussing feedback, we're dealing with the previous organ's knowledge that the problem that needs to be addressed is being addressed, and this feedback is performed by short and long loop feedback systems.
Short loop feedback generally refers to a pituitary hormone providing negative feedback to the hypothalamus, inhibiting secretion of the releasing hormone. For example, growth hormone releasing hormone (GHRH) from the hypothalamus is inhibited by growth hormone (GH) that has been released from the pituitary.
Long loop feedback refers to the hormone that was released from the peripheral endocrine glands inhibiting pituitary and/or hypothalamic secretion of releasing hormones. For example, insulin-like growth factor 1 (IGF-1) is stimulated to be released by GH. IGF-1, in turn, inhibits GHRH and GH secretion by long loop feedback.
A more minor sort of feedback that we have overlooked is the concept of ultrashort loop feedback, where a hormone from the hypothalamus inhibits its own secretion. GHRH is an example of this effect, where its presence in the blood prevents the release of more GHRH.
I hope this helps!