I _have_ heard them being used to try and create a more interactive, engaging environment for the students. Typically they're used something like this:
The teacher explains something, then asks a question that you can correctly answer if you understood the explanation. There's N answers available; the question + multiple choice answers are on the current slide.
Students then group up into small-ish groups (4 people or so, maybe less) and each group discusses the question & comes up with an answer, and then they use the clicker to make their choice.
Once all the groups have had a chance to answer the teacher displays a bar chart / histogram showing how many groups chose each answer.
The next part I'm not 100% clear on the details, but the bar chart points the students in the right direction AND provides feedback for the instructor. For example, if pretty much everyone got the right answer then the teacher can give the groups that didn't choose the right answer a couple minutes to re-discuss and/or ask questions. If lotsa' students got the wrong answer then the teacher can go back and clarify stuff, etc, etc.
So yeah - the point of clickers is to transform a passive "listen to the teacher lecture" experience into something that is more interactive and engaging.
In terms of apps - I don't use clickers myself (I teach smaller classes), but if I wanted to I'd definitely use an app for this. I suspect that people still using physical clickers got started with them and are continuing to use them. Personally I'd get my college to buy a classroom set for the students to borrow each class (or to checkout for the semester/quarter/term) but there's overhead with that, too
