These errors occur during the period when VPOP3 is trying to establish a connection to your ISP's POP3 mail server to receive incoming mail. They can mean that you have entered the POP3 Server address incorrectly, or that there is a problem with the network, or that your ISP's mail server is not working properly.
If the message text is
Pop3 Client not started - Couldn't connect to server XXXX (YY)
Then this means that VPOP3 was having a problem connecting to the In Mail entry called 'XXXX'.
Following this text there should be a further description of the specific error which occurred. See here for a description of those errors.