Salesforce1 is a new platform, complete with a host of new APIs and mobile UI tools.
To oversimplify it, it's taking the Chatter mobile app, which up until this point has just been an app running on closed source code and building it into a platform, while really blowing out its capabilities. It's built on the premise that our business lives are increasingly happening in the feed. Every action from a like to a comment, now has a public API and method call behind it. More than just Chatter however, it's allows you to embed your business applications either through Visualforce or custom publisher actions (with you app hosted wherever). Salesforce1 will offer custom branding, administrator configuration, and allow for installable apps. 3rd party sales tools, service tools, marketing apps will be able to plug right into this framework.
More than just mobile, while it is the focus, Salesforce1 represents a new API-first mentality at Salesforce.com. Every action, interface, and new feature is built on top of a public API that developers can also wield and consume. Think about a list view in Salesforce, it's not something you can build without some pretty deep customization and code of your own. This UI component is not built on a public API. This is the old paradigm of Salesforce.com and Salesforce1 is the new one.
Worth referencing here is the Salesforce1 App Developer Guide and a full listing of Salesforce1 APIs