apsd -- Apple Push Notification service daemon
By sampling the running process in the Activity Monitor I get this:
Code Type: X86-64
Parent Process: launchd 
The process is launched at system boot and remains constantly active. Every 15 minutes a log message is generated in system.log file(Viewable by the Console app), containing a warning that there is a Unrecognized leaf certificate. I've used tcpdump/Wireshark to sample the network traffic four individual times(just to be sure).
Destination: 4-courier.push.apple.com (220.127.116.11)
Destination: 14-courier.push.apple.com (18.104.22.168)
Destination: 44-courier.push.apple.com (22.214.171.124)
Destination: 23-courier.push.apple.com (126.96.36.199)
The IP addresses really do belong to Apple,
NetRange: 188.8.131.52 - 184.108.40.206
OrgName: Apple Inc.
Address: 20400 Stevens Creek Blvd., City Center Bldg 3
The traffic was(as expected) SSL on custom
port 5223 as described here: http://support.apple.com/kb/HT6175
TCP or UDP: TCP
Service or Protocol Name: Apple Push Notification Service
Service Name: -
Used by / Additional information: iCloud DAV Services (Contacts, Calendars, and Bookmarks), APNS, FaceTime, Game Center, Photo Stream, Back to My Mac
The certificate that the server is sending however looks like this:
Verified by: Entrust Certification Authority - L1C
C (Country): US
ST (State): California
L (Locality): Cupertino
O (Organization): Apple Inc.
CN (Common Name): courier.push.apple.com
Apple obviously changed something in the load balancing scheme because apsd is never connecting directly to the domain courier.push.apple.com. And the service is not reachable through that domain if one attempts to connect manually from the browser (as https://courier.push.apple.com:5223) either.
However on mentioned subdomains:
It is possible and the error appears: "This certificate is not valid(host name mismatch)". What I believe is happening is that apsd is reporting the same thing, but the developers decided to write that in the logs as "Unrecognized leaf certificate".
Apple should create a new certificate that includes a wildcard (CN (Common Name): *courier.push.apple.com) to correct this issue. I've submitted a Feedback/Bug Report on http://www.apple.com/feedback/macosx.html
But this could be more serious then just an annoying log message, if apsd is actually ignoring the wrong certificate and just continuing to work!
Continued here: Is Apple's push notification service implementation vulnerable to a MitM attack