Re-iterating what jtheman said with a little more explanation:
Create a file named .htaccess with the contents:
RewriteEngine on
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ page.php?businessname=$1 [L]
You need, of course, the ability to have directory level .htaccess enabled - you're using a VPS so you should be able to do this if it is not already enabled.
So let me explain what each line will do.
RewriteEngine on
Turns on the ability to URL re-write
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
Tells Apache not to re-direct files that exist in the directory already
RewriteRule ^(.*)$ page.php?businessname=$1 [L]
This is where the magic happens.
^(.*)$
this part is like a regular expression match. It will tell Apache to collect any URLs that have any characters within them and redirect them to page.php?businessname=(.*)
So, if you post:
www.website.com/stackover
It will really be sending: www.website.com/page.php?businessname=stackover
Then you can just use $_GET[businessname]
to dynamically update the page.
Hope this helps!