xmlns - proper usage

I've been looking everywhere to find the answer to - what is xmlns and
how should one use it properly? I haven't got very much farther than
it's the namespace...  Most xslt documents just use
xmlns:xsl="http://www.w3.org/1999/XSL/Transform.  There isn't much at
that url.

I have an xml file, which includes an xmlns of its own, which points
to a .xsd file, which does what  you'd expect - defines variable names
& such. The xmlns is defined in the top-level element:

<Query Response xmlns="http://some_uri/API_Response.xsd">

I couldn't get the stylesheets to work until I removed the xmlns from
the .xml document.

Could somebody shed light on this?
Thank you!