Why can I see '/' in a file manager when my device is not rooted?
I thought that root was required to do this.


That's not quite right. Any user can see that directory, but only root can write to it. Directories lower down the hierarchy such as /data/data are not world-readable, so while you'll be able to see that that directory exists, you won't be able to see its contents on an unrooted device.

Some file managers choose not to offer the option to display system directories like the root directory unless the device is rooted, simply because it's not very useful to do so when you can't see the contents of some of its subdirectories or change it.