Breast lesion segmentation in ultrasound (US) videos is essential for diagnosing and treating axillary lymph node metastasis. However, the lack of a well-established and large-scale ultrasound video dataset with high-quality annotations has posed a persistent challenge for the research community. To overcome this issue, we meticulously curated a US video breast lesion segmentation dataset comprising 572 videos and 34,300 annotated frames, covering a wide range of realistic clinical scenarios. Furthermore, we propose a novel frequency and localization feature aggregation network (FLA-Net) that learns temporal features from the frequency domain and predicts additional lesion location positions to assist with breast lesion segmentation. We also devise a localization-based contrastive loss to reduce the lesion location distance between neighboring video frames within the same video and enlarge the location distances between frames from different ultrasound videos. Our experiments on our annotated dataset and two public video polyp segmentation datasets demonstrate that our proposed FLA-Net achieves state-of-the-art performance in breast lesion segmentation in US videos and video polyp segmentation while significantly reducing time and space complexity. Our model and dataset are available at https://github.com/jhl-Det/FLA-Net.