John, cobranding isn't a technical term; it's a marketing technique. It comes up frequently in Web site design and construction because site builders are called upon to provide the necessary tech support for cobranding.
The best way to explain it is by example.
Imagine that Site A has a lot of traffic but needs more content and functionality. Site B has a great concept, great content, and great functionality ... but nobody has ever heard of it.
So site B offers to sell content to Site A. Site A doesn't want to pay very much for it, and Site B isn't really sure it wants to sell the content, because Site B's creators believe they have the key to riches and happiness if only enough people would hear about their great ideas.
So they do a deal: Site A gets the content, but in a cobranded deal: the pages will contain both Site A's brand and Site B's brand. Site B might get some money (or it might not); it definitely gets public exposure for the brand it is trying to build.
You can find examples of this on every major Web site; sometimes the source branding is strong, sometimes it's weak.
Now, if I can attempt to make this relevant to a PHP discussion board, here are the technical implications.
A lot of this content isn't really being shipped around. Quite often it's being served by Site B, but in Site A's look and feel, or in a blended look and feel.
If Site B does a dozen or so of these deals, it's created for itself one King Hell of a content-management problem. How do you support a dozen completely different presentations of the same content?
With PHP, you can keep the content and the presentation reasonably separated.
By passing around some cobranding variables (in cookies, with referer strings, embedded in URLs, or in PHP sessions) you can conditionally place the right branding and/or use the right layouts on the pages.