Native is not a name, it is a condition. Native means here that it is built in... It naturally lives on your phone.
It is Hard Coded into the OS and non-removable.
Go to Settings > email + accounts > add > add in an account by filling in the required info > after an account is added > go to your apps list and scroll to the account type (Gmail, Gmail2, Outlook, etc.) > the mail App automagically makes an inbox for you > pin that to start.
No matter what email account you add, it will make an inbox. You can get to other folders in the email address by tapping overflow (...) and folders to navigate to Sent, Drafts, etc. Every account you add will look the same and act the same when opened: be it Yahoo, Outlook, Live, Gmail, private mail server... Because each and every one created uses native Mail App.
Go to Settings > email + accounts > tap an account name to open options including what to sync (mail, calendar, contacts)
Go to Settings > email + accounts > hold down on an account name and tap sync from the pop up menu to sync the entire account
Just like every email integrates into Mail... all those account contacts integrate into native Contacts App... all those account calendars integrate into Calendar App.