Hello,
I keep seeing that colleges want you to show that you have taken full advantage of the opportunities available to you...what exactly does this mean (for a highly competitive public school in the Bay Area) and how does one accomplish this?
"Taking advantage of available opportunities" can mean a couple of different things. Academically, it means that you should strive to take advanced classes and excel at them. This doesn't mean that you should overload yourself with AP classes just for the sake of having taken them, but it does mean that you should take honors or advanced classes in your areas of interest. For example, when I was in my (highly competitive) public high school, I opted to continue taking Chinese my senior year instead of taking AP Statistics (since the class schedules conflicted), even though it meant I couldn't take any other math classes (since I'd finished up BC Calc the year before).
There's also the extracurriculars piece, although again, you shouldn't just do extracurricular activities for the sake of doing them; instead, focus your time and energy on activities that you are passionate about. Don't waste your time trying to be "well-rounded" for the sake of college applications or do a bunch of unrelated activities and hope colleges can string them together into a coherent narrative of someone who's good at things. If you haven't already, I would highly recommend reading our article on how to get into Harvard and the Ivy League, which goes into greater detail about showing colleges what you have to offer.