When a piece of work, email or note is assigned to you, it will trigger a notification in Triage, and also appear in the assignee's to-do list. A Task, however, will not trigger a notification in Triage, but it will appear in the assignee’s To-do.

Any new to-do item will be highlighted in your to-do list, and will appear at the top of the corresponding to-do period.

Further reading:
Why don't I get a triage notification when a Task is assigned to me?