How do externalities actually create market failure?

Market failure is the misallocation of resources by the price mechanism.
I know the idea of externalities but how exactly do externalities create market failure. My book says something regarding how prices don't reflect the costs and benefits to society.

Can anyone explain this please? Also what else is there to externalities, I've learnt the production/consumption diagrams and the policies that can combat externalities. But should I know the diagrams for each policy?

Cheers

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