Browse the files created on a device by the iOS application I'm developing, on workstation?

In Xcode's Organiser, go to your device's Summary tab. Find your application in the list, and click the disclosure triangle. Under it, you should see an icon saying "Application Data". Click the down pointing arrow to download the data, and it'll prompt you for somewhere to save it.

In Xcode 5, listed under your device in Organizer, click on "Applications" and you can see "Data files in Sandbox" in the bottom half of the window.

In Xcode 6, go to Window -> Devices, select the device, select the app name under Installed Apps, click the settings gearbox, then select Download container.... In finder, double finger tap the package and select Show package contents.

In Xcode 6, open the Devices window:

Then, select the app (in Installed Apps) and then click the gear icon and select Download Container.

Pls note, that you can view contents of downloaded .xcappdata container by right click on it and select "Show Package Contents"