The message only shows once, but Apple is hoping it'll be enough to get developers on the 64-bit bandwagon. This means that 32-bit apps will run normally for the time being.
Apple has not said exactly when it will stop supporting 32-bit apps, and it's likely to still be some way off in the future - but that day is still drawing closer.
Ars Technica says that Mac users running macOS 10.13.4 will receive a one-time alert tomorrow that triggers when a 32-bit app is opened. Further, it also includes a previous warning from Apple to the developers that High Sierra will be the last version to use 32-bit apps. While support for 64-bit Intel apps was not simultaneous with Apple's transition to Intel-powered processors, support for 64-bit apps has existed for over a decade.
Presumably, the switch will officially be made in macOS 10.14, but Apple maintains that "final transition dates have not yet been established". Even so, it's not likely Apple will immediately cut off support willy-nilly. Apple has required new Mac App Store app submissions and app updates to be 64-bit since January 1 of this year.
In addition to receiving the alert once when a 32-bit app is launched, Apple also lets users check for 64-bit compatibility through the system report feature.
Apple explained that it is making the break from the 32-bit apps because of the advancing technology.
This break with compatibility for the very first version of watchOS is an indication that Apple intends to keep rushing forward with Apple Watch, and that watchOS 5 will be more than just a minor upgrade.
Start by navigating to the Apple logo in the top-left corner of the screen, clicking on it, and selecting "About This Mac". The company has now started informing Mac users that 32-bit app support is going to end in the near future. Scroll to Software, select Applications, and then check the 64-bit field. The bar on 32-bit iOS apps was one of the key reasons the number of iOS apps in the App Store fell a year ago. There could be one on the developer's website, or in Apple's App Store. In case of macOS, the company already stopped accepting similar apps to Mac App Store. The pop-up says that the app needs to be updated.