<p>What is the difference between a <strong><em>framework</em></strong> and a <strong><em>library</em></strong>? </p>

<p>I always thought of a library as a set of objects and functions that focuses on solving a particular problem or a specific area of application development (i.e. database access); and a framework on the other hand as a collection of libraries centered on a particular methodology (i.e. MVC) and which covers all areas of application development.</p>

A
library
performs specific, well-defined operations.
A
framework
is a skeleton where the application defines the "meat" of the operation by filling out the skeleton.  The skeleton still has code to link up the parts but the most important work is done by the application.
Examples of libraries:
Network protocols, compression, image manipulation, string utilities, regular expression evaluation, math.  Operations are self-contained.
Examples of frameworks:
Web application system, Plug-in manager, GUI system.  The framework defines the concept but the application defines the fundamental functionality that end-users care about.