At last year's Worlwide Developer's Conference (WWDC), Apple announced to Mac app developers that macOS High Sierra "will be the last macOS release to support 32-bit apps without compromise." Now, in the macOS High Sierra 10.13.4 beta, Apple is notifying users of the impending change, too.
In the beta release notes, Apple says:
To prepare for a future release of macOS in which 32-bit software will no longer run without compromise, starting in macOS High Sierra 10.13.4, a user is notified on the launch of an app that depends on 32-bit software. The alert appears only once per app.