what is connected app in salesforce - Salesforce Globe For You
Connected App:A connected app is a framework that helps external application to integrate with salesforce using API's and standard protocols like SAML,OAuth and OpenID connect.
These protocols are used by connected App to authenticate,authorize and provide single sign-on (SSO) for external apps.
The connected app captures metadata about the external app such as which protocol the external app uses and where it runs etc and then provides the same information to salesforce.Salesforce then grants access to external application to access it's data by attaching some policies that define access restrictions.
Uses of connected App:
1)Access Data with API integration: if web based or mobile applications wants to pull data from salesforce,you can use connected app as client to request the data.
2)Integrate service providers with salesforce.
3)provide authorization for extrnal API gateways
4)Manage access to third party apps.
Go through the following trialhead for more details
https://trailhead.salesforce.com/content/learn/modules/connected-app-basics