What is the technology used to prompt for passwords on an public wifi network When connecting to the internet via a public wifi hotspot on a mac or ipad, rather than the simple wifi password requested by a home router, a new 'sheet' or dialog is displayed to log into the network, often with some branding of the hotspot's owner. An example in the UK would be the Virgin hotspots on the London underground network.

What is the technology used to initiate and display this authentication mechanism and is there a way to have the device / desktop remember the password? A workaround is to open a browser which can remember the password but its very irritating that the password is not remembered and there is no option to remember it.
As far as I know, it is not called "Push notifcation" as indicated in earlier answer.

The correct name for this is a "Captive portal".

The technology is simply that the user's requests are redirected to a specific web page until the user has authenticated (or whatever requirements the specific provider has).

The redirection can technically be done via HTTP (i.e. some kind of HTTP proxy), via ICMP redirects or via sending back fake DNS replies.

Apple has added detection of these captive portals to Mac OS X. After connecting to a WiFi system, Mac OS X will try to access an address at Apple - if it succeeds it assumes the user has general access to the internet.

If not, it will assume a captive portal is in place, and popup a window for the user to authenticate to the network.