What's this feature - "Add Named Library"?

What is something that you can attach jars/classes to
it and be reuse in other projects? I thought it was
this, but I couldn't get this to work.

That was the way it worked in earlier versions of IDEA (such as Ariadna). There was a discussion going on here that resulted in the conclusion that this feature is quite useless. So they changed it now in a way that those named libraries are local to a module.
There are two other possbilities to define libraries. These can be found on the order-tab of the main module project properties page. They are "Add Application Library" and "Add Project Library". I haven't tried them but I guess that "Add Application Library" can be used to define global libraries.

What is something that you can attach jars/classes to
it and be reuse in other projects? I thought it was
this, but I couldn't get this to work.

"Add Named Library" - is a way to structure jars/directories (in Libraries
tab of Main Module). When mutliple module projects become available it
likely be a bit changed.

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Best regards,
Dmitry Peshehonov
JetBrains, Inc, http://www.intellij.com