As others have mentioned, showing and not telling means bringing personality and creativity to your statement and using examples and experiences to make the account worth reading.
What I don’t think it means, though, is that your entire application should come together as a “coherent story” that tells some neat, clean story about your interests and hobbies. I don’t think any person fits in a box that neatly, much less a teenager in high school who doesn’t have it all figured out yet.
The reason I bring this up is because I think a lot of college students think they have to carefully curate their classes, activities, and hobbies to fit into some narrow narrative, perhaps cutting out other things they are interested in but that don’t fit the “story” they are trying to tell. Or they get to junior and senior year and panic because, much like the majority of people, their interests are kind of all over the place.
You’re a multi-faced person and it is OK for you to have many interests! It is also OK for you to explore those many interests in high school, college, and beyond.
That doesn’t mean you can’t illustrate a story out what you have done - but it does mean that you may need to think more deeply about your story and what it says about you. Maybe the story isn’t “I love biology” (which honestly is pretty simplistic) but “I am deeply interested in how things work, what turns the gears of the natural world,” which explores your stint in psychology club, your volunteer work at an environmental nonprofit, and AP physics classes. Maybe your story is even that you like taking risks and exploring new things, which explains your propensity to throw yourself into something new and work deeply in it for some period of time.