As with the WiFi settings in Windows Phone 8.0, WiFi Sense settings are used to set-up and configure connections to WiFi hotspots, a critical feature for a smartphone if you want to off-load data from your cellular connection (or don't have a cellular connection).
However, as can be seen in the video, Windows Phone 8.1 introduces three new features: automatic re-enabling of WiFi connectivity, automatic sign-in to hotspots, and sharing of WiFi hotspots with friends. Each feature has the underlying aim of making it more likely that your phone will use available WiFi connections.
automatic re-enabling of WiFi connectivity
After switching WiFi off, it is now possible to set WiFi to be automatically switched back on after a set period of time (choice of 1 hour, 4 hours, 1 day), something that's very useful if you want to avoid using WiFi for a certain amount of time (e.g. when walking around town when your phone tries to log-on to multiple similarly named hotspots).
automatic sign-in to hotspots (WiFi Sense)
The feature that gives WiFi Sense its new name is the ability to sign into certain types of WiFi hotspot automatically. Typically, when using a public WiFi hotspot it is necessary to accept terms and conditions and (sometimes) enter a name, email address, and phone number, before you can start using the connection. This isn't usually a big deal on a laptop, but can be more fiddly on a smartphone. What WiFi Sense does is to accept terms and conditions and enter necessary information on your behalf (i.e. automatically). The result of this is that, when out and about, your phone is more likely to be able to user a WiFi hotspot, thus saving you from using cellular data.
It's not clear which hotspots are going to be support by WiFi Sense, but the likelihood is it will be popular large scale free hotspot networks, such as those provided by MacDonalds and Starbucks. Microsoft wll presumably also try to do this for other free hotspots too, but connectivity may depend on the software being able to recognise how to automate the terms and condition / information collection process.
Potentially, Microsoft could extend this feature to commercial WiFi networks that require user authentication, but this is unlikely to be present in the first implementation of WiFi Sense.
sharing of WiFi hotspots with friends
WiFi Sense also makes it easier to share WiFi hotspot details with friends. This will enable friends who have WiFi Sense on their devices to use the hotspot (WiFi connections) that you have configured on your device (and set as allowed for sharing), but without sharing (or having to enter) the necessary passwords. This would mean a friend could use your home WiFi connection, without you having to give them the password details (and with zero set up for them).
The WiFi Sense settings allows you to specify which group of friends get access to shared WiFi connections. You can opt to share with Outlook.com contact (default contact provider), Skype contacts, and / or Facebook friends, with the last two requiring prompted permission.