Comps appears from Google Books to have emerged in the 1940s out of ad-agency jargon. The earliest use I've found is this:
The illustrations in “Advertising Layout” are the work of the five top advertising artists in America. Many of the layouts shown are the original “roughs” and “comps” directly from the visualizer’s drawing board. – ad for Advertising Layout by Richard S. Chenault in the magazine Advertising & Selling, 1946.
Putting the term in quotes suggests that it was a relatively novel use then. Earlier uses of comps in these contexts refer to people, the compositors.
When I took a course in layout back in the 60s the standard sequence for developing a (print) design was Sketch, Rough, Comp (the first stage you show a client), Final. In my shop today we never see a “sketch” or a “rough” – a website designer just produces three or four suggested “designs” and the client picks one that's tweaked and serves as the basis for the final. But they're pretty much what we called “comps” in my youth, and I wouldn't be surprised to hear that the term has lingered in other shops.
I remembered this as a short form of “composition”; but I now find that Wikipedia defines the term otherwise:
In graphic design and advertising, a comprehensive layout or comprehensive, usually shortened to comp, is the page layout of a proposed design as initially presented by the designer to a client, showing the relative positions of text and illustrations before the final content of those elements has been decided upon. The comp thus serves as a draft of the final layout, and (if approved) is used as guide for further design changes and, ultimately, production.