When a page is built, it's as though the HTML structure of the page is laid out in a number of layers, one above the other.
The very bottom layer is the body, which as Juri says, covers the entire browser window (top to bottom, left to right). The immediate layer above that is the PageWrapper layer, which is blue in Juri's screen shot. On your site, that is specified to be 1000px wide and central. You've made it transparent, so I can see the lower body layer through your transparent upper PageWrapper layer. The PageWrapper is generally what you consider the "footprint" of your site.
Inside the PageWrapper container, is the HeaderWrapper container with all the Header structure. This layer sits above the PageWrapper layer. In your case it's also transparent, so the body layer is still visible through the PageWrapper and the Header elements as well.
What size of image should I ask her to prepare for me? I want it to span the entire site. I'm using the Perfection template. This is for my site [Domain Private].
Generally, full screen images on SBI templates (that go from far left to far right of a monitor) are capped at 1600px.
At this width, most monitors will see a full screen image, but most people won't see all of it. For example, if I use a Sony laptop, width 1366px, I won't see the extreme 117px on the outside left or right. (1600-1366 = 234/2 =117)
There is a whole sub-story about mapping device pixels to CSS pixels, but that's for another time.
And when you say 'and how you want it to display.' Does this mean bits will be cut off on certain devices?
Anything outside of the PageWrapper boundary is not shown on most portrait tablets and mobile phones. Given how the majority of viewers are now on mobile devices, most of them do not see the outside sections of a fixed background image. Your desktop viewers will see it, but how much they see depends on how you've set the image to display (cover or contain etc) https://www.w3schools.com/cssref/css3_pr_background-size.asp
Here's what's visible of your image at the moment on an iPhone 5.