Since the speaker didn't expound at all on what he meant by aerodynamics, an explanation has to come from two places:
- What happened on-screen just before he says this
- How a cape would affect flying in a world where birds and airplanes and hanggliders work.
Just before that line is uttered, Kara is in a car chase, and completely misses a hard left turn. She ends up plowing into a fence on the side of the road. Thus, we can assume that having the cape, in-universe, helps her navigate while flying.
This, of course, just begs the question. It doesn't explain why it helps her navigate. For that, we get no help from Supergirl, but we can can picture what a cape should do if attached to a flying thing.
Mostly, it changes the way drag builds up behind her. The cape, being separate and elevated slightly from her body, might be expected to behave in a way similar to a spoiler on a car. We know that spoilers are used in high-performance cars partly to help them make turns at high speed. There are two problems here, though. First, the rear spoilers work by pushing the rear of the car down, increasing traction on the road and decreasing drift. For Kara, though, she's not in contact with the ground, so the effect of a spoiler would be to shove her into the ground — rather counterproductive.
More importantly, a spoiler is a fixed addition to a car. Since the cape moves with air flow, however, the dynamics are much more complex (and I couldn't find a good analysis of them online.) It would create some effect on the drag; it's possible that it may help slow Kara down when she banks, or disrupts the air flow around her, in such a way that it increases her maneuverability.
Or, at least, it would if it wasn't so small and thin. Given how flimsy her cape is, the actual amount of air displaced by it, and the change in drag relative to the rest of her body, probably isn't enough to make any difference at all.
For reference: at no point do I think any Superman story explained the cape as aiding in flight: it was almost always there for sentimental and/or decorative reasons. Out-of-universe, it was meant to mimic the look of circus strong-men.