Can someone explain to me what does it mean to "install Ubuntu in the cloud"?
How does that differ from signing up with a VPS with any hosting company?
Really trying to understand what this means and how it's different from normal web hosting.
The "Ubuntu in the cloud" server install option will install Eucalyptus and Walrus and other software necessary for you to build your own local version of Amazon's EC2/S3 compute/storage farm.
This might be helpful if you need to support a lot of virtual machines - maybe for students to learn system administration, or to keep different applications separated from one another.
Ubuntu's cloud system uses the same API that Amazon does - so if you write software that uses one, it can use the other pretty easily.
The server installation disk is pretty much unrelated to using Amazon EC2 instances with Ubuntu - if you want a Ubuntu EC2, use one of the pre-existing machine images and don't worry about the installer CD.
Here is a walkthrough of a local Ubuntu private/local cloud installation, if you want to see what would happen if you chose that option.