OnConnect is a TIdServerThreadEvent property that represents the event handler signalled when a new client connection is connected to the server. 

OnConnect receives the TIdContext that represents the executable task for the client connection. OnConnect allows processing that occurs after the client connection has been accepted by a listener thread, and before execution of the TIdContext instance. 

Applications must assign a TIdServerThreadEvent event handler procedure to OnConnect to allow responding to the event notification. OnConnect is triggered by the protected procedure in the server assigned to the TIdContext.OnBeforeRun event handler.

TIdContext 

TIdContext.OnBeforeRun 

TIdServerThreadEvent