(1) For Windows file management favorites, see 
Windows Libraries.
(2) A collection of pre-written software routines that programmers use when writing an application.  The routines in the library are called for with commands in the source code of the program.  The library routines are linked to the program either when it is compiled or at runtime.  See 
source code.
In the Unix, Linux and Mac worlds, a library is called a "library."  In the Windows world, it is known as a "dynamic link library" (DLL), and there may be hundreds or thousands of library files in any given computer.  See 
DLL and 
class library.
(3) Any electronic collection of files or links to files.  For example, the Library in Apple's iTunes software includes music, movies, TV shows, books, apps, ringtones and Internet radio links.
(4) A device that manages multiple storage modules and provides one or more drives for reading and writing.  See 
tape library, 
disk library and 
optical disc library.
(5) Offline storage.  See 
data library.