phpMyAdmin does not do any formatting to your records.
The trouble is that you have newlines ("\n") in your text, and you're expecting them to display in your browser as newlines. Browsers don't do that -- you have to use HTML to format your text. If you do View > Source in the browser, you'll see that the newlines are there, they just aren't displayed (because they're not supposed to be). That's where nl2br() comes in. It converts newlines to HTML line breaks so they'll be displayed.