I hope the Title question says it all. There are two 'Library' directories in my OS X 10.11 installation, one being /Library/, the other being /System/Library/. What is there difference between those?
As in all the Unix system, there are two type of
One specific for the user and the other for the entire system and so all the users of the machine.
In particular for OS X: the Macintosh HD version is the actual computer Library, while, the home folder version is specific to your user account.
Here an example to help you understand how to use it:
/System/Library is a place to store fonts, screen savers, Dashboard widgets, and all other things that all local users need access to.
~/Library is for your own user account only (cache and preference files, widgets for your use only, etc).
EDIT: taken from here, a complete overview of all the possible library folders in a Mac OS X system:
The user library, ~/Library, stores per-user settings etc.
The local library, /Library, stores computer-wide settings and all-users content etc. I call this the "local" library, because in NextStep it was /Local/Library, but you'll see all sorts of other names for it, such as the root library, computer library, ...
The network library, /Network/Library would store settings shared by all computers in a network domain -- if a network domain admin set one up, which nobody does anymore...
The system library, /System/Library, stores the base settings, resources, etc that come with OS X. In theory, you shouldn't change anything in here.
/System/Library is for stuff installed by Apple, native to the OS
/Library is for things that pertain to all users on a computer.
And for completeness (although not mentioned in the question):
~/Library is where things specific to a particular user go.