macOS has been 64-bit and 32-bit since 2005, and generally speaking if you purchased a new Mac in 2007 or later, its processor is 64-bit. This was the statement it released for the goal: "The last macOS release to support 32-bit apps without compromise is macOS High Sierra". On the other hand, pressing OK will close the alert box and launch the app normally because the current macOS version still has support for 32-bit apps. The alert pops up once per app and serves as notification of Apple's pending transition to 64-bit technology. Also, even Apple hasn't moved all its apps to 64-bit. For this, one needs to go to the Apple menu and select This Mac, and then click the System Report button.
If you're interested in going through your Applications folder and checking each app to see if it's 32- or 64-bit, here's how. One of the items is 64-bit (Intel). Like, the 64-bit architecture enables taking advantage of more memory than its 32-bit counterpart.
There's no harm in using 32-bit apps, but Apple wants developers to utilize modern hardware features that only work with 64-bit apps.
Apple's warning message also includes a link that takes the Mac users to the Apple support page for further information.
By nagging users well in advance, Apple will presumably be hoping that developers will be bombarded with support tickets from users, forcing them to take action sooner rather than later. The pop-up says that the app needs to be updated. But for those who have been using Macs for years, download software from outside the Mac App Store, or perhaps have built their own apps, there's a chance that at least some of the programs on their computers are running in 32-bit.
While Apple continues the transition from 32-bit to 64-bit only on the Mac, Apple has already completed the transition on iOS. Second, desktop apps are downloaded from several other sources apart from the MacOS App Store.