My doctor said my mammogram was suspicious -- what did she mean?

Needs evaluation. Anything outside of normal or benign needs to be evaluated by further imaging and/or a second opinion with a surgeon specializing in breast disease. The use of the term "suspicious" often means a biopsy may be needed to rule out cancer. Always good to get an accurate diagnosis then you can decide how you want to deal with health challenges.
Depends. If it was a screening, it means you need to return for more imaging because a radiologist saw something that didn't look completely normal. If there was a suspicious finding on follow-up imaging, you will need a biopsy to get an answer.
Suspicious finding. Technically a suspicious(BIRADS category 4) breast lesion carries a chance of malignancy between 2-95%. This is unfortunately a wide range, but this classification is mandated by the Mammography Quality Standards Act(MQSA). Generally these lesions require biopsy, and as mentioned in another answer, about 75% of the biopsies turn out to be benign.