$(x_1, y_1)$ or $(x_{min}, y_{min})$ generally refers to the coordinate of the top-left of the bounding box, as the x-coordinate goes from left to right and the y-coordinate goes from top to bottom in computer-vision.

However, note that the bounding box coordinate labeling may be different depending on what convention the dataset/model is following.

For pascal_voc convention, this is $(x_{min}, y_{min}, x_{max}, y_{max})$

For coco convention, this is $(x_{min}, y_{min}, \text{width}, \text{height})$

For yolo, this is $(x_{center}, y_{center}, \text{width}, \text{height})$ normalized

You may refer to the below link for more details https://albumentations.ai/docs/getting_started/bounding_boxes_augmentation/