Click Don't Upgrade unless you want to commit to using Apple's Two-factor authentication with Apple ID. Once you upgrade to using it, there is no way back.
Why is it important? Read about it in this Apple Support article: Two-factor authentication for Apple ID.
The salient point is that you must absolutely, positively have a "trusted device" that can receive SMS text message codes. Preferably that would be an iPhone, but it can be any device capable of receiving text messages—usually any cell phone. If you should ever lose that "trusted device" you'd better have a backup plan. If you don't have a backup plan it is conceivable to lose control of your Apple ID forever. That's a bad place to be and Apple won't be able to help.
That's the bad news. The good news (and the motivation behind 2FA) is that using it makes theft of your Apple ID credentials effectively impossible. And if you think Apple ID theft isn't a big deal just have a look at this Discussions area: Apple ID. I used to participate in it but the number of people who evidently succumb to Apple ID theft every day (through phishing scams for example) became overwhelming. Even I couldn't keep up.
The other good news is that two-factor authentication for Apple ID works really well and is as unobtrusive as it could be.
So unless and until you familiarize yourself with Two-factor authentication continue to click Don't Upgrade. You will have to answer the dumb security questions once in a while. Upgrade to two-factor when you finally get tired of doing that. I did and it's ok. Wish it weren't necessary.
And Apple isn't the only one depending on it. Lots of banks / credit card companies / insurance companies require two-factor authentication now, and you don't have a choice.