About the opposites and the reader
I agree that it is problematic setting up 'clarity' and 'sounding smarter' as opposites, but I get that you do not intend for this to be the case.
With clarity you seemingly mean 'ease of understanding for the unspecialised reader' and with sounding smart you mean diving into 'advanced content' or 'subject-technical language', and as with many other things, it's probably the somewhat frustrating answer that applies; "It's a matter of balance."
If it's a technical college - which we might assume, since you're writing about the thing that you are - it seems to me, that you could absolutely expect the reader to know about, at least on a basic level, the things you write about. Unless you're writing about absolute cutting-edge technology or research, chances are that it would have to get very technical or specific in order for it to be too much.
About the overall purpose of the text you're writing
I'm not personally familiar with the sort of application/text you're writing, but I would absolutely expect any school or educational institution to look at it as an example of how you approach and work with a given topic or phenomena. If this is the case, they are most likely to look at how well you can communicate or introduce the topic or 'problem area' and how your text is relevant based on this, and how well you show academic prowess or potential. The latter (in most of europe at least) focuses a lot on critical/creative (as in explorative as well as solution-oriented) thinking and the ability to communicate clearly why 'your' perspective adds value to your field, and, potentially, how your thoughts or suggestions may; 1: make clear how a solution or approach/understanding is flawed, 2: open up new areas of the field or 3: create solutions for an existing issue, or one that 'you' have discovered.
This doesn't mean, that you have to be a genius or have already found or made a major breakthrough - not at all. But, and again this is my take, your letter should to some degree show, that you could at some point be part of that type of work.
So what should you do?
If you've been given a prompt/assignment/task/problem formulation, pay close attention to what they ask, and try to follow their guidelines as closely as possible. In the end, the college is interested in students who show that they can follow 'their guidelines' - even if you may at some point see them as outdated (but that's a different 'problem').
Apart from that, I would say give'm hell. Unless it becomes totally unclear why you're working on/writing about the thing that you are, the advanced and technical parts show what you actually know and understand. From there, if you have the chance, have someone read it and see if they struggle to understand the point of the text - not whether they understand the advanced parts. Perhaps they can approach it as sci-fi, where it's not important they they actually know how the technical parts really work, but they understand that you're highlighting and working with something important or at least relevant.
