Videos come in a range of framerates.
Live TV is normally 50Hz (Europe) or 59.94Hz (US).
Cinema releases (and so BluRays and DVDs are usually 23.97Hz.
There also exist 24Hz, 25Hz, 30Hz and 60Hz
By default kodi runs at the framerate reported as preferred by the display. Normally 50Hz in Europe and 60Hz in US.
The differing framerates of the video and display causes a subtle judder effect, most noticeable on panning shots (it just looks a little jerky). Many people don’t really notice this, but some fine it quite jarring.
“adjust display refresh rate” means kodi will try to pick a better HDMI mode for each video it plays.
It results in smoother video, but TVs are generally slow to switch modes, causing a blank screen for a few seconds on playback start and stop. The best TVs takes about a second to switch. The worst may take 7 seconds or longer.
This setting has always been “opt in”, so users who don’t explore the settings will have it disabled.
Sam made a change to Krypton to enable this by default. As there have been a number of reports about this behaviour being unwanted I think this change will be reverted in the future.
Personally I always enable it manually. I prefer the smoother video and am willing to put up with the blank screen delay at start and stop of video playback, but each user has different priorities. I would recommend that it is a setting users experiment with and are aware of the two options.