Basically Shared library works as a container for anything you can use as general things for your campaigns: for example, you can write some ads that should be included in different ad groups (so that you don't have to copy them separately), you can use one budget for a few campaigns, you can choose negative keywords for different campaigns.
Moreover, you set up remarketing lists in Shared library. It helps you save time while managing your AdWords account in some cases.
Just adding more point in addition to the great point received by Milda.
You can also create a list of negative keywords and Placement exclusion list in shared library that you can directly exclude from the multiple campaigns. Thus it saves time for you to optimize the campaigns.
You can also set shared budget for multiple campaigns from here.
You can follow all features available in Shared Library in the link
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