The ListItemEntityTypeFullName property (SP.Data.ProjectPolicyItemListItem in the previous example) is especially important if you want to create and update list items. This value must be passed as the type property in the metadata that you pass in the body of the HTTP request whenever you create and update list items.
For example, when you want to update list items in a list called "MyCustomList" you need to know the ListItemEntityTypeFullName of the list items before hand. In this case, it will be SP.Data.MyCustomListListItem. Most examples around the internet do this by querying the list first and then getting the ListItemEntityTypeFullName property from it and using that in the call to update the list items.
If you do not specify the ListItemEntityTypeFullName, you get this error
An entry without a type name was found, but no expected type was specified. To allow entries without type information, the expected type must also be specified when the model is specified
The good news is that you only need to use the entity type full name is when you are using "application/json;odata=verbose" as your Accept and Content-Type headers.
If you are using "application/json;odata=nometadata" in your Accept, and Content-Type headers, then you do not need the ListItemEntityTypeFullName as well.
Here is are a couple of quick gists I have put together to show how we can create and update list items without specifying the ListItemEntityTypeFullName. I should mention I have tested these only in SharePoint Online at the time of this writing: