The ~/Library is where per user information is kept. For example, your email, your application preferences, iPhone/iPad backups, browser bookmarks, etc... That way your settings are separate from other users that may share your Mac (think a family sharing the same Mac).
The /Library is for common to everyone things, such as fonts, browser extensions, application shared code libraries, system wide network preferences, etc...
The ~/Library was hidden because too many users would go mess with thing in there, or delete things, and then call customer support or go to the Genius bar complaining they lost important things. ~/Library is still there, it is just less likely to have customers do things in there that will damage their system because they do not understand.
You can access ~/Library by using Finder -> Go menu -> Hold Option Key -> Library