I just recently run in to this very same issue and asked the same question from the support. At the time of the writing Vagrant Cloud Beta does not offer box file hosting (this is expected to change very soon). Instead you have to save the box-file somewhere in the internet and provide the url to that location. Note the file can't be behind authentication.
Update 28th May 2014
The following note has appeared to Vagrant Cloud Beta Help-section:
A core part of this service will be hosting of actual box files. This is being tested internally at the time of the beta launch, and will likely be a paid feature due to high bandwidth costs.
The privacy issue is still unaddressed in the Private Boxes-documentation.
Update 30th May 2014
HashiCorp has announced yesterday the end of Beta and a bunch of new features including box hosting. See their announcement for the details: Vagrant Cloud: Organizations, Box Hosting and the end of Beta.