Note: this is a placeholder article so I can create a bit.ly link for an upcoming MSDN Magazine article that will point to the real documentation for this feature. Those docs are currently in progress and will likely be available by the time the article is published. But we have to finish the galley proof for the print magazine now, hence the placeholder!
Until just recently, here in the summer of 2015, the Visual Studio Online build system didn't have support for cross-platform apps like those created with Xamarin. That support has now been added.
When you're on VSO's Build tab for a project, you'll see "Build definitions" and "XAML definitions." The latter, XAML definitions, are those that worked with the previous build system that does not have cross-platform support.
If you create a new definition with the big green +, you'll be presented with the new list of templates:
Clearly you can see the options for building Xamarin.Android and Xamarin.iOS projects, along with the Xcode option for building a straight iOS native app.
What about Xamarin for Windows? I'm told you can use the Visual Studio template for that, but I haven't tried this myself. In any case, when you use one of the Xamarin templates you'll be required to enter your Xamarin credentials to activate the necessary platform licenses:
Anyway, that's all I'll say for now because I haven't tried out all of this myself. Again, proper documentation will be appearing soon on MSDN for all the details.