You should be able to use these wherever you need to connect to a web service. The HTTPCaller is one example. If you turn on authentication one of the methods is Web Connection. There may also be Readers and Writers that allow you to connect to a web service as a source/destination.
Having said that, I don't know what the current state of these is. I suspect we haven't implemented them as fully as we intended to and that there will be a lot of updates still to come. There's this whole "cloud as a drive" idea that is almost certainly going to be implemented at some point - where you define (say) Google Drive connections and can use them as the source for any Reader.
In short, right now they probably won't do a lot. In the future, they should be incredibly important.
I can provide more details.
Yes, the web connections as they ship in FME 2016.1 are the tip of the iceberg in terms of the plumbing we've been laying in FME for supporting the coming tsunami of web data services.
In FME 2017 we intend to expose these more and more in nice easy to use packages.
In FME 2016.1 they are already *usable*, if not immediately obviously *useful*.
You can use them to provide authentication to http://* web requests. The primary place one might do this is in the HTTPCaller -- as Mark suggests. It does completely work, but you're left to working with the REST API of the service in question at a very primitive level.
You can also use this if you ever are using http://* as the location of your source dataset. Provided you know the right URL for say a file in Google Drive, you can put that in the source dataset, and the provide an authenticated Google DRive connection in the parameters. It will just work.
Awkward we know. But it works. And just watch how this will jump to life in FME 2017...