Sending out mail uses the Simple Mail Transfer Protocol (SMTP). This protocol basically sends all your mail trough port 25 to a server (like Gmail and Hotmail/Outlook) where it is then sent to the person you wanted it to go to.
If none of your emails are being sent out then this protocol is probably being blocked. Your router/modem is probably blocking or interfering with traffic through port 25. If it isn't your router/modem, then your ADSL probably just needs to be resynced or have the port recreated. This is done on Afrihost's side. Contact them for further support.
If the problem is on your side, then you'll have to reset your router/modem, or go through it's settings to find the problem.
If you haven't tempered with any of the router settings before the problem occurred it is likely that the problem doesn't lie on your side. I have had a similar issue a two times before with Afrihost, where all http (web browsing) was blocked. They can have the problem solved from their side in a few minutes.