As @uSlackr has said, it is the configuration that Windows will use when DHCP is unavailable. What should probably be added is that, despite the MS article's suggestion, this is almost never really used or needed for home users.
The Microsoft article states:
When you are in the office, the computer uses a DHCP-allocated TCP/IP configuration. When you are at home (where you do not have access to a DHCP server), the computer automatically uses the alternative configuration.
However, it is the reverse which I expect is more likely to be true. Most home networking hardware these days includes a DHCP server, and a majority of them even allow for DHCP address reservations. So, there's rarely a time (unless you're particularly paranoid) where a home network will ever actually need to use static IP addresses.
On the other hand there are some business networks which, for some reason or another, prefer static IP addressing over DHCP. So, you'll probably end up actually using DHCP for your home network and the "Alternate Configuration" for work.
One other rare case where the "Alternate Configuration" can be handy is for direct PC-to-PC connections, or deliberately isolated, temporary networks where there is not going to be a DHCP server available either by design or just for simplicity. While you could just use APIPA, it is much easier to communicate using known, familiar IP addresses. If it is common for you to use your computer in such situations, having the "Alternate Configuration" as a fall-back definitely beats manually switching the settings on the "General" tab every time.
The only scenario I can think of which would be useful for home users is for exactly when, as @uSlackr put it, "DHCP fails". It is not uncommon, with some SOHO networking equipment, for the DHCP service to occasionally malfunction and require a reboot of the device to resume operation. Generally during these times, a static IP configuration can work around the problem until you have a good opportunity to take the network down for the reboot.