A connected app is an application that allows an external application to integrate with Salesforce using APIs and standard protocols like SAML, OAuth, and OpenID Connect. Connected apps use these protocols to authorize, authenticate, and provide SSO for external apps.
For example, after logging in to your Salesforce mobile app, you will see your data from your Salesforce org, you’re using a connected app.
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Also, check out this video on Salesforce: