So many metaphors in these answers :-D
When you write your code for different projects, you try to avoid repeating the same thing again and again - so you write them once and reuse this code as a module. Or - if someone, somewhere already did it - you borrow another person's code and use it. That's what we call libraries: simple code for a group of typical exercises. There are libraries for mathematical calculations, for database operations and so on. So again:
When you make bigger and bigger projects, you would like to use not only well-written, specific code libraries but other tools too. You want the best libraries in a pack, a whole environment, maybe even use it by several different languages. A framework usually provide:
Examples:
Controversies: Definition of 'framework' is not really strict. My examples were extreme, there are many in between. There are huge libraries which are called frameworks by professionals or their creators, because they are so big, they are to organize whole projects, or simply for marketing reasons. The best you can do is to handle them as libraries except if there is a very good reason to accept they are something more.
I think "frameworks" involve abstracting workflow, like how construction workers will use scaffolding (an abstraction of a structure) to support them while they work on various parts of a building:

and "libraries" are closer to what they sound like: rather than being a collection of books, they're a collection of common solutions to problems. Just like how you might walk into a library and select just the right book to read you can use a code library like a bunch of pre-written solutions that you can look around for and select and put to use:
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It's possible to make use of both frameworks and libraries, but you have to make sure that these solutions actually help what you're working on rather than making it awkward.
Picking the wrong framework is like having scaffolds that go to nowhere, but don't get you close what where you need to be to do your work. Picking the wrong library is like having a bunch of great solutions you don't need, and still not being able to find anything for what you do need.
Over time, you can build your own frameworks and put your own solutions into libraries that you can use when solving familiar problems.
Frameworks are like parents, they give structure to your life and make things easier to do.
Libraries are like tools, someone builds a cool thing that lets you do cool stuff and makes it easy to plug 'n play with your app so it can do the cool stuff too.
Framework is a Lego set or set of pencils and a paper. Just assemble blocks together or draw whatever you want on a paper with a ready tools.

Library is a Wizzard's hat. You put something into it and it gives you what you want. Like reheating a pizza in a microwave.

Library is a ready toy while framework is a tool to help you make your own toy.
Not everything can be explained like you're 5, but I'll give it a try:
Framework - chain of build time + run time scripts/functions that is opinionated and encapsulates your entire application/business logic. You embed your logic inside the 'mold' framework gives you. You usually do not want to isolate parts of the framework. And if you have previous work, it usually requires a 'surgical operation' to embed that work inside the framework.
Library - Usually a main object/constructor/function that harbors collection of functions that does one thing and one thing well. You are free to mix and match and use parts of it.
I'm not going to say pros and cons. Because I believe I should be able to give the message without mudslinging on either approach (and this is the ethically optimal one I guess).
But if you ask my orientation, I'm more of a library guy with no extremes.
Tommy Hodgins
CSS & Element Queries
Purvi Barot
Software Engineer
Library : A well defined set of instructions which provide unique properties and behavior to your data.
Framework : A collection of libraries which provide unique properties and behavior to your application.
When you have a library you need to understand the functionality of each method and it is relatively hard to create complex interactions.Frameworks, on the other hand, contain the basic flow and since you only need to plug in your behaviour.
If you don't like the jQuery date picker library, you can replace it with another date picker such as bootstrap date picker.
If you don't like Angular on which you built your software, you can not replace it with any other framework. You need to rewrite your entire code base.