A typical (and proven) marketing and sales strategy by Apple:
(1) Realize that there is still a significantly profitable segment in the smaller screen iPhone. Cover that base as well. Well aware that this is not a miniaturised version of a flagship model (6S). More of an (already varied) option for every size needs and costs. To have the best/newest technology - buyers will need to look at the 6S/S Plus. Buyers don't like the size - they can consider the SE. They may seriously consider the SE even if the tech is not up-to-date, but at least it is almost similar to flagship model in some specs.
(2) Reduce cost in terms of new physical hardware redesign, but make it refreshed with new internal. All other accessories can be reused/or modified slightly. Case makers/other accessory makers rejoice.
(3) Reduce the price, make it an entry level iPhone. Make it even cheaper - get people re-interested on all old case, improved specs because of the 'value'. Value is compared against the similarly sized previous model (5S) and the present phone with an almost similar internal (6/6S).
Better than the old, but slightly lesser than the new. Got people thinking (and considering).
(4) Keep prices low for the 16 GB. But knew very well that a few buyers will know that is hardly enough. In the end, a lot of people will be getting the configuration with higher memory capacity - and they are willing to pay for this reason. Apple makes a lot of money.
(5) Knew very well people choose Apple over the whole experience. Specs may be less updated, prices may be more but it runs on a an acclaimed iOS and has the prolific Apps Store. Some people will buy an Apple just for this.
Personally, I have been holding myself from getting a 6 due to the size as well, but did not get a replacement for my broken 5S as I have wanted a better camera. I end up getting small android because of that. And while I am interested to get an Apple Watch, I still don't like to carry the bigger 6 around - so I was kinda waiting for Apple to release a smaller sized iPhone.
The SE provoked my interest once again even though I would prefer a radical new physical look. I still remember the awesome feel and has always prefer iOS over Android. Basically, Apple is drawing me to get this SE based on the points I mentioned above.
Though I must say, the Galaxy S7 is really impressive. If Samsung suddenly announced an S7 Mini, it will be a tough one for me!