Fibroglandular Tissue. Facts About Fibroglandular Tissue in Breasts. Fibroglandular tissue in breasts is a very common condition and is known as Fibrocystic Breast Disease. This disease is characterized by having fibroglandular tissue present in the breast.ibroglandular Tissue. Facts About Fibroglandular Tissue in Breasts. Fibroglandular tissue in breasts is a very common condition and is known as Fibrocystic Breast Disease. This disease is characterized by having fibroglandular tissue present in the breast.