> I am trying to understand what exactly does 'xmlns' do in 
>  <xsl:stylesheet xmlns:xsl="http://www.w3.org/XSL/Transform/1.0">

it declares the xml namespace (hence xmlns) which has name the URL
http://www.w3.org/XSL/Transform/1.0
is to be associated with elements and attributes that have the prefix
xsl:

You could just as well have

<jha:stylesheet xmlns:jha="http://www.w3.org/XSL/Transform/1.0">

and then use <jha:apply-templates etc, the XSL engine would treat
this exactly the same as a stylesheet using xsl:.

> Does the proper execution of the styleseet depend on the specified url
> being up  and running?

No, it is just a name.

> Does the xsl processor download something from this site?

No.

David


 XSL-List info and archive:  http://www.mulberrytech.com/xsl/xsl-list