What is the most likely diagnosis for a mobile and well-defined breast mass in a young woman?

A mobile and well-defined breast mass in a young woman is most likely indicative of a fibroadenoma. Fibroadenomas are benign tumors that commonly occur in women in their late teens to early thirties. These masses are typically discrete, palpable, and painless, often described by patients as feeling like a "slippery marble" within the breast tissue.

The characteristic features of fibroadenomas, such as their mobility and well-defined edges, distinguish them from malignant processes. In contrast, infiltrating ductal carcinoma is often associated with irregular borders and may be fixed to surrounding tissues, making it a less likely diagnosis in this scenario. Cystosarcoma phyllodes and lipomas, while also potential considerations, are less common in this demographic and usually present with different characteristics than those seen in fibroadenomas.

Overall, the clinical presentation and demographic information support the diagnosis of a fibroadenoma in this case.