Print. Arachnoid cysts are cysts, not tumors. They are fluid-filled sacs that develop between the brain/spinal cord and a membrane called the arachnoid membrane, one of three membranes that cover the brain and spinal cord.rint. Arachnoid cysts are cysts, not tumors. They are fluid-filled sacs that develop between the brain/spinal cord and a membrane called the arachnoid membrane, one of three membranes that cover the brain and spinal cord.