I think one of the key distinctions here, that the other answers do not explicitly point out, is that there is a difference between list Views and list Forms.
Lists come with three default Forms, the "New" form, the "Display" form, and the "Edit" form. Forms:
- Show only the data for a single list item.
- Show the data in a two column table, where each field/column is represented as a row, and the field/column names are in the left hand column, and the value of that field for that particular list item is in the right hand column, either displayed just as text (in the Display form), or in editable controls (for the "New" or "Edit" forms).
List Views, on the other hand:
- Show data from multiple list items at the same time
- Are organized in a multi-column table, where each list item is represented as a row in the table, and the fields/columns of the list are represented as the columns of that table.
"All Items" is the main default view of any list. You can also create custom views that apply filtering and sorting, and define which fields/columns you actually want to see as the columns of the table shown in that view.
The screen shot posted by the OP is the web part property pane of a List View Web Part. This web part is used to show views. If there were any custom views set up on that list, they would be available as options in the highlighted drop-down, along with "All Items", "Summary View" and "Current View".
However, the "New" form, being that it is a Form and not a View, is naturally not included in the options for the List View Web Part.
The other answers here provide some good options if the OP is looking to get users to the "New" form for the list from somewhere other than going straight to the list and clicking "new item".
- Copy the URL of the "New" form for that list and use it in a link on another page somewhere.
- Figure out how to expose that form through an iFrame (or some other means) on a different page.
However, you are not going to be able to select and show the "New" form (or either of the other forms) using the List View Web Part.