You have a post on Mac OS X 10.4 Tiger that shares via an Ethernet cable, its direct internet connection via a modem or via Wi-Fi, with a second post-Ubuntu Linux. When retrieving mail from the Linux desktop, an error message will appear if the firewall is active and you have not taken the time to open ports 110 and 25 which are normally blocked at the exit Mac.
However, they must be open so that messages can be retrieved and sent from the desktop Linux.
In Mac OS X, open System Preferences -> Sharing -> Fire Cup. Click New in the Port Name menu, select Other and write for example "mail".
In the category of TCP port numbers, enter: 110, 25. Close. Restart the firewall, restart Internet sharing (by clicking on the button of the window Internet Sharing).
You should meet more worries. Obviously, the procedure to open ports is also valid in other cases.