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Although this answer isn't specific to PHP, a framework is typically a system where the programmer "fills in the blanks" of the code provided by the framework. So to rephrase that.. a framework provides the structure of the program for you, then you fill in the information it needs.
On the other hand, a library is just a collection of prewritten code/utilities that can be used at your leisure where ever you need them. With libraries there is no particular structure, just a "library" of code to use however needed.