Inbox is a special storage for notifications. When someone @mentions you, assigns you a task or another important action happens, you receive notifications. These notifications are stored in Inbox unless you open and/or archive them. Notifications are grouped by date: Today, Yesterday, This month.
In Archive, notifications are kept for a month. You can archive a notification by opening it. Some notification types (mentions and task assignments) can be archived only by clicking the Archive button. For your ease, archive all notifications with a special Archive All button.
In case there are several notifications for the same task, they are grouped. To see the list of all notifications, click on it, and the list will drop down. You will see the number of unseen notifications near the task name.