FYI - this is the Mail, Contacts and Calendar discussions area for the iPhone.
You should have posted your question here instead.
http://discussions.apple.com/forum.jspa?forumID=753
The Mail application's Get Mail button does exactly what it indicates - it checks the incoming mail server for all enabled accounts for new mail.
There is no difference between selecting this button and your automatic checking for new mail setting.
Mail > Preferences > Accounts under the Advanced tab for the account preferences > Include when automatically checking for new mail and Mail > Preferences > General > Check for new mail.
What type of account - POP or IMAP?
Have you checked the account via webmail access using a browser to confirm there are new messages available at the server which have not been received by the Mail application?