What does it mean that my activity is shared with my teacher?
It means the teacher has enabled Live mode for this widget.
Teachers can choose to enable live activity tracking for their widgets. When enabled, a teacher can monitor the current state (currently filled in answers, last activity time, ...) of widgets that have been recently accessed, so they can quickly help where needed. Only the teacher that shared the widget (i.e. created the widget link) can track this information.