For the question, I assume that you're not working with any framework. Given this, I'll give you a simple answer.
Steps:
1 - Get the username out of the URL.
2 - Generate the view dynamically.
Explanation:
1 - I would recommend using a query string of the following format: mywebsite.com/page.php?username=certainusername (instead of using a #)
Then you can use $_GET to obtain the username (Please, read more about the security implications: http://php.net/manual/en/reserved.variables.get.php).
2 - If you're using PHP to generate the HTML code directly, the only thing that you need to do is:
... HTML in here ...
data="http://www.twitch.tv/widgets/live_embed_player.swf?channel=<?php echo $username; ?>"
... more HTML ...
(Assuming that the variable $username contains the username obtained from the URL).
This is a very simple scenario and there are a lot of other things to consider that are out of the scope of the question.