Any time you receive a new diagnosis, in this case of the ovarian cysts, it is important to fully understand the condition. To that end, I think it is best you speak to your primary doctor
about these questions. Alternatively, an ob/gyn could be of help as a specialist in the field.
In general, ovarian cysts are separate and mostly unrelated to ovarian cancer. Ovarian cysts, depending on your age, are often functional. That is, the form during the high estrogen stage of your menstrual cycle and then disappear during the later stage of the cycle. They can become painful and / or bleed--but these normally resolve on there own. Often your doctor will recommend a repeat ultrasound
in a few months to make sure they do reduce or disappear. Other causes of ovarian cysts can be from a benign malgrowth--such as a dermoid cyst. Other possibilities include endometriomas--which is when the uterine lining is out of position in the ovary. Finally, if your ovaries have multiple cysts- your may have Polycystic Ovarian Syndrome--which is an endocrinological disorder that is related to diabetes. Around 15-20% of reproductive age women have cysts. Cancers are often solid and not cystic (cyst implies hollow). Rarely cancers can be cystic. Your doctor may have you get a repeat ultrasound to see if the cyst does not go away (which may be more concerning). In general, if the cyst are functional--this does not change your risk for ovarian cancer and would be unrelated to cancer.
Ovarian cancer is a rare but important disorder. In general, cysts alone would be an unusual, but not impossible, presentation for cancer. Discuss this with your doctor.