A library is a collection of routines that’s usually meant to be shared for multiple programs. Generally this involves providing a file (usually in the form of a DLL or a COM Component) that gets distributed with each program that uses it. With more modern development technology, it’s usually more than just a collection of global routines, but a collection of classes for use in Object Oriented programs.
A framework is a library, but it usually much more. Sometimes a framework is not distributed as a single file (or even multiple files) with each program that uses it. A framework is usually a large component that’s installed on a machine, and that one installed instance is used by multiple programs on the machine. An update to the framework affects all programs on the machine that use it. Some examples of frameworks are:
There are thousands of frameworks available. Some are free, some need to be purchased, some are part of your Operating System.
A Framework generally consists of lots and lots of functionality, providing a complete solution for a programmer to code a certain type of capability into their program.