Your app will still work after the alert appears; the main objective of the alert is to encourage users to update the app to a current 64-bit version. It's not clear if Apple is planning to turn off 32-bit support in macOS High Sierra or if that's going to be reserved for future versions of the operating system.
For developers, the lure to update their apps to 64-bit is obvious - if Apple stops letting them run, then that's an income stream gone, right there.
"The technologies that define today's Mac experience - such as Metal graphics acceleration - work only with 64-bit apps. This is done via a one-time alert that appears when you launch a 32-bit app", Apple continued. Next to a field "64-bit (Intel)', it will say "Yes" if it is a 64-bit app and 'No" if it's a 32-bit app. It's part of an overall move to remove 32-bit application support from the operating system at some undetermined point in the future. For business users, the Blue Jeans and Cisco WebEx teleconferencing clients are still only available as 32-bit apps. To ensure that the apps you purchase are as advanced as the Mac you run them on, all future Mac software will eventually be required to be 64-bit. "No" means the app is 32-bit and needs to be updated, while "Yes" means it is 64-bit and will work just fine without further action from the developer.
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New apps that were to be submitted to the Mac App Store in January 2018 had to be of the 64-bit variety and developers would also have to upgrade all existing apps in the App Store to 64-bit by June 2018 if they wanted their apps to remain approved for listing. The company has already stopped accepting any new apps that use 32-bit technology into its Mac App Store. The A7 chip, which powered the 2013 iPhone 5S, was the first 64-bit mobile processor. At the same time, it'll be easier for Apple to maintain the apps.
Like with iOS, the goal is likely to ultimately not support older 32-bit apps on macOS at all. Presently, the App Store does not accept submissions of 32-bit apps for macOS. Further, a user also gets the option to delete it or keep it, even though the app can't be used, notes CNET.
Users who wish to make certain their applications are 64-bit can check them by hitting the System Report button in the About This Mac menu.