There are two reminders that can be triggered:
1) You can set up email reminders to be sent (optional when creating task
2) You are notified the day it is due in the notification center (See screenshot from my Hubspot instance. Again this happens the day it is due (happens automatically). Screenshot below
Here is the support document for tasks - https://knowledge.hubspot.com/articles/kcs_article/tasks/use-tasks
Screenshot:
