What the gamma calibration test shows
A patch of alternating black and white lines averages to half the light output of white, whatever the display’s gamma. A solid grey does not — the value that looks like half depends entirely on the transfer curve. Put them side by side and the one that matches tells you the curve.
The standard target is 2.2, which is what sRGB assumes and what almost all content is authored for. A display running at 2.4 makes shadows too dark; one at 1.8 makes them washed out.
How to read the gamma patches
Step back from the screen — at least an arm and a half — and half close your eyes so the lines blur into a solid tone. Find the pair where the striped half and the solid half become indistinguishable. The number underneath it is your gamma.
Use the selector to mark the one that matched. Your choice is stored in the address bar, so a reading is a link you can keep or send to someone.
What this test cannot tell you
Only valid at a device pixel ratio of 1. On a HiDPI or scaled display each "line" covers more than one physical pixel or gets resampled, the average is no longer half, and every reading is wrong. The page checks and tells you when this applies — most sites offering this test do not.