i'm guessing here (and i shouldn't be) but by default mail won't send outside your network, so you really need to configure a proper postfix server to do this.
Thankfully this is rather straight forward
www.postfix.org has stacks of guides / howtos.
But i could be wrong and mail will do it by default; also there is another concern, if your mail client is not properly configured other servers will bounce it, issues like a fqdn (fully qualified domain name) and such may arrise.