I just completed a module about mySalesforce. So I’ll just summarise what I’ve learned.
mySaleforce is a product which allows you to create a fully-branded version of Salesforce1. It only impacts the visual appearance of the mobile app and functions exactly the same.
This can have the benefit of increased adoption of the app. It also looks a bit more professional or prestigious.
You will have to supply your own branding such as logos etc. It involves downloading a managed package, without which the app won’t work.
Behind the scenes, Salesforce submits the app to the Android and Apple app stores.