Exim log shows delivery to local user first and then delivery to recipient

Exim log shows delivery to local user first and then delivery to recipient

When I send an email (using the mail command via command line) from a user
on my VPS to any other address, I have noticed that exim logs a delivery
to the user that is sending the email first, and then logs the delivery to
the recipient.
I am creating an exim log parser, mainly so that I have a reason to
dissect and better understand exim, and I am just trying to understand
what is going on here.
Here are some of the tests that I have done and the resulting logs:
Sending an email from testlinuxuser@mydomain.com to externalemail@gmail.com
2013-08-13 02:32:02 1V94Ow-0006HC-Fx <= testlinuxuser@mydomain.com
U=testlinuxuser P=local S=518
2013-08-13 02:32:02 1V94Ow-0006HC-Fx gmail-smtp-in.l.google.com
[2607:f8b0:400d:c00::1a] Network is unreachable
2013-08-13 02:32:03 1V94Ow-0006HC-Fx => externalemail@gmail.com
R=dnslookup T=remote_smtp H=gmail-smtp-in.l.google.com [173.194.76.27]
X=TLS1.2:RSA_ARCFOUR_SHA1:128 DN="C=US,ST=California,L=Mountain
View,O=Google Inc,CN=mx.google.com"
2013-08-13 02:32:03 1V94Ow-0006HC-Fx Completed
Sending an email from testlinuxuser@mydomain.com to
testlinuxuser@mydomain.com
2013-08-13 03:14:57 1V954T-0006LQ-3s <= testlinuxuser@mydomain.com
U=testlinuxuser P=local S=506
2013-08-13 03:14:57 1V954T-0006LQ-3s => testlinuxuser
<testlinuxuser@mydomain.com> R=local_user T=mail_spool
2013-08-13 03:14:57 1V954T-0006LQ-3s Completed
I could go on with the other scenarios, but I think you'll get the point.
I have tried searching for the local protocol that exim is referencing
there,(P=local) but that has not resulted in anything for me.
The very first log always says that the message is delivered to the email
account that is sending the message. I thought that maybe that is because
it was saving a copy of the email to a list of sent emails or something. I
checked and I have not been able to find that. I have read the exim docs
and I have not found any mention of this yet. Does anyone know what that
log is actually saying that exim is doing there?
Using Ubuntu 13.04 Server on an AWS EC2 instance with Exim4, installed
with apt-get and configured with the dpkg-reconfigure exim4-config command
for my domain.