Integrating a software into another website page sounds like a daunting task. However, it's really quite easy with MyBB. Here's all you have to do:
Above the rest of your website code, put this.
<?php define('IN_MYBB',1); require_once('path_to_mybb/global.php');
and with that, you have access to MyBB! you can use its $db object, $mybb->settings variables, and even $mybb->user information (given that you have a cookie domain and directory that allow your new application access to the cookies)
It's much easier than you think. Learn how to do even more integration in my next ProTip.