Intrinsic factors are those factors or characteristics that are part of the system or product being tested. An intrinsic factor is an internal factor. So, for a typical commerce site, the HTML page code that the browser uses to display the shopping cart pages is intrinsic to the site: change the page code and the site itself is changed. The code logic called by a submit button is intrinsic to the site.
Extrinsic factors are external to the site or application. Your crappy computer with only 8 megs of RAM is extrinsic to the site, so your home computer can crash without affecting the commerce site, and adding more memory to your computer doesn't mean a whit to the commerce site or its functioning.
Given a severe shortage of test time, focus first on factors intrinsic to the site:
does the site work?
do the functions work? (again with the functionality, because it is so basic)
do the links work?
are the files present and accounted for?
are the graphics MIME types correct? (I used to think that this couldn't be screwed up)
Once the intrinsic factors are squared away, then start on the extrinsic points:
cross-browser and cross-platform compatibility
clients with cookies disabled
clients with javascript disabled
monitor resolution
browser sizing
provide payment information
connection speed differences
The point here is that with myriad possible client configurations and user-defined environmental factors to think about, think first about those that relate to the product or application itself. When you run out of time, better to know that the system works rather than that all monitor resolutions safely render the main pages.