As @greg-hewgill already mentioned in the comments, the
Received:-header is added by every mail server which handles a mail and places there information where and when the mail came from. For example, here're some lines (from one of my posts at serverfault):
Received: from scipy.org (unknown [126.96.36.199])
by hostname.example.net (Postfix) with ESMTP id 0ED6022427
for <firstname.lastname@example.org>; Fri, 5 Dec 2014 14:30:18 +0100 (CET)
Received: from scipy.org (localhost.localdomain [127.0.0.1])
by scipy.org (Postfix) with ESMTP id CA29E327C6;
Fri, 5 Dec 2014 07:30:07 -0600 (CST)
Received: from plane.gmane.org (plane.gmane.org [188.8.131.52])
by scipy.org (Postfix) with ESMTP id 1D4FD32728
for <email@example.com>; Fri, 5 Dec 2014 07:30:05 -0600 (CST)
Thus you need to hide your own IP, if you don't have admin rights for the mailserver you are using (then it's easy to solve). This is typical application of anonymization like with TOR. You can also go with a VPN (Virtual Private Network), thus tunnelling all your internet data through a secure channel to some other endpoint of your VPN provider and showing the mailserver this IP instead of your private one.
But you need to make sure, that in both variants, the client could reveal more informations, like it's version and other things. So to be fully anonymous, there are more steps to take. But it's not the right place here and I'm sure you'll find enough information in the internet. Otherwise, ask your specific question on Information Security @ SE.