Dear wayfleah: A complex cyst describes a structure that has both solid and cystic (fluid filled) components. The concern is around the solid part of the structure. Sometimes a surgeon will recommend removal to be certain that there is no abnormal cell growth and that these are, in fact, cysts.
I had the same medical problem as yours about 6 weeks back. One 2 cm. complex cyst, got it aspirated and results were all benign. I still consulted a breast surgeon, who advised surgery , excisional biopsy to rule out the 2% chance that something other than cystic is going on. I went & got second & third opinions. Finally got the surgery done, it does have cancer. Excisional biopsy surgery is a minor problem , but what you find after that could either give you peace of mind or put you on the right track to save your life.