Prior to lightning experience enablement in Winter '16, I used to use a handy trick when demonstrating the Salesforce One mobile application to prospective clients. By simply appending '/one/one.app' in the url you could view the application in your browser. e.g. https://ap1.salesforce.com/one/one.app
This was also useful when running training sessions via a large monitor or projector. It would be quite difficult to demonstrate to a room of people using a mobile device.