The mind-made body is not clearly defined in the early texts. However, it refers to something similar to what in Western esoteric traditions is called the “astral body” or “subtle body” (sukhumarūpa).
It’s a mental image that corresponds with the physical body. However, in the Buddhist sense, it is part of rūpa, i.e. the physical realm, even though it is created by and perceived by the mind. This is because it has physical properties like shape, position, color, etc. It takes on the same physical shape and attributes as the coarse material (oḷārika) body.
The idea is, I think, that the mind-made body is the felt or perceived body, i.e. the physical body as experienced internally. Normally we have an inner map or idea of the body which matches the externally perceived body quite well; but this is not always the case. Consider the well known phenomenon of phantom limbs. For an amputee, the phantom limb they can experience would be their mind-made body, which doesn’t completely correspond with the coarse body.
For advanced meditators, in certain cases it becomes possible to detach these two bodies much more radically, enabling the phenomena of astral projection and the like.