A connector defines a service or data source that you can access with Power Apps or Power Automate. There are hundreds of pre-defined connectors to be used and if you need to connect to a service or data source for which there is no connector, you have the possibility to create a Custom Connector. Examples of connectors are for the different Office 365 service, e.g. for sending e-mails and connecting to SharePoint, Microsoft Dataverse (currently there is two; CDS and CDS Current environment), Twitter, Dropbox etc.
The connectors have triggers and actions. Triggers are used to initiate a Power Automate flow and the actions are used for different operations e.g. read and write data. You can also connect to on-premises sources by setting up an on-premise data gateway.