The Tasks button lets you access the list of created tasks.
A work item most probably contains some tasks that must be completed by you or your team in order to accomplish the objective of that work item. For example, if you have a Loan Review process, it is very likely that you have a task that revolves around collecting the requestor financial information, such as income, the amount requested, nationality, etc.
When you click on Tasks the inbox loads the list of tasks that are for me, and it expands the list of other available filters for tasks. The button for creating a new task is also shown. But keep in mind that this newly created task is somehow special: it creates what is called an ad hoc task. An ad hoc task is different from a task in the sense that it does not belong to the hierarchy of a work item: it is not part of a process or a case. Also, an ad hoc task does not have a form associated to it. It only contains four fields: name of the task, assignee, due date, and description (only the name is required).
The Tasks Inbox shows you tasks based on the filter you have selected in the expanded list. For example, if the For me filter is selected in the submenu, you only see tasks you are assigned to.
The ordering of the tasks depends on the filter you have selected:
For the filters For me, Unassigned, or Open tasks the order is the combination of: by due date ascending, by priority descending and by creation time descending. This means that tasks that have their due date close are on top, then for the ones that have the same due date the ones with highest priority and then the ones that were most recently created.
For the filter Completed tasks the order is by completion date descending, meaning that most recently completed tasks are shown on top of the list.
For the filter All tasks the order is by creation date descending, meaning that most recently created tasks are shown on top of the list.