Hello,
At a minimum the number of computers and servers involved looks something like this :
Your Computer -> Your ISP's SMTP Relay -> The recipients incoming mail server / pop server -> Their computer
It sounds like you are sending OK to your ISP's SMTP relay, but your ISP server is unable to reach and relay the email to the recipients incoming mail server.
SMTP Relays will generally try to relay an email for somewhere between several hours and a couple days before giving up and bouncing the email back to the original sender. In this case your ISP is also sending you a notice before it gives up to let you know that it hasn't been able to relay the email to the destination yet but it's going to continue trying for a while longer.
If you copy and paste one of the bounce messages we can help you figure out if it looks like a problem with your ISP's SMTP Relay (not likely, but possible), or the incoming mail server for the person you are trying to send the email to (most likely)
-Raymond