I maintain a firewall for our corporate network and management asked for a mDNS proxy so that their iPhones on our Wi-Fi network could see our Airprint printers on the Ethernet LAN. I regularly see firewall log entries for traffic from desktops on the LAN to iPhones on the Wi-Fi network. At first it seemed random, but then I realised that the desktops and the iPhones were assigned to the same user in each case. The iPhones have presumably been paired with the desktop (iTunes) in the past and the iPhones are using mDNS / Bonjour to look for desktops that they have been previously paired with. The desktops are communicating from ports in the range of 60289 to 62089 and always direct to port 62078 on the iPhone. We don't have iPads on our network (as far as I know!), but from the Original Poster, it appears that this may also be the case with iPads.
A little bit of digging found an article about Juice Jacking : http://www.zdziarski.com/blog/?p=2345
So this port is used for iPhone or iPad Wi-Fi synching, as mentioned by rjw1678. Once a pairing has been established with a computer, then your iPhone or iPad will always try to pair with this device until such time as you perform a factory restore on the iPhone / iPad.