Warning: this is rather tricky…
What to see & do, Part 1
When the demo has loaded, you see a largish disk on the left changing its colour between green and a dark red. [Best deselect the “min. motion” checkbox to avoid detraction.] Now move the slider up, and notice that the red becomes brighter, the green darker; move it back down; nothing to write home about, so far, I agree. Look for the three buttons labeled “0”, “10” and “50”; press “0”. Now the flicker is much faster. Again slowly move the slider up, and notice (if you have normal colour vision) that the disk turns into a (nearly) non-flickering dark yellow version; moving further up increases the flicker again while the colour turns more reddish.
[Instead of moving the slider with the mouse, you can use the up/down keyboard arrows.]
What we have here is called “heterochromatic flicker fusion”. Normally we think of flicker when light's switching between on and off, here it is switching between two different colours (thus “heterochromatic”). When these colours do only differ in hue, not in brightness, the disk does not seem to flicker any more at some position of the slider (apart from occasional artifacts traceable to some computer intricacy). This condition is called “equiluminance”.
When the frame delay is at “0”, meaning a different disk colour at every frame, the flicker frequency is 30 Hz. With luminance flicker, this is quite visible (normal flicker fusion frequeny being ≈50 Hz), but there pure colour flicker is already fused. This can be used to find the point where two colours are of equal luminance – interesting effects do occur there, as demonstrated here and here.
What to see & do, Part 2
Another way to find out if two colours are of equal luminance is the “minimum motion” technique, as cleverly developed by Stuart Anstis & Pat Cavanagh (1983). Click on the checkbox “min. motion” and observe a the right something like a wheel. This wheel rotates when we're off equiluminance either left or right, and comes to an unrestful standstill around equiluminance, which happens to be the same position when you see minimum flicker in the left disk.
The explanation of “minimum motion” is somewhat involved, and has to do with a (nearly) colour blind motion system choosing the best luminance match from frame to frame (which, BTW, also explains the waggon wheel effect). Details can be seen in the original paper by A&C (1983) or in Raphael & MacLeod (2011, Fig. 3).
Comparing these two methods to achieve equiluminance reveals that (1) the two equiluminance points are very close, if not identical, and (2) minimum motion technique is far more sensitive, having a very narrow neutral zone. No wonder the latter is frequently used in vision experiments when you want to adjust for equiluminance. Finally, there are many confounding factors: increasing the number of sectors slightly shifts the equiluminance point, the point of regard has an influence (e.g., look at the left edge and adjust for equiluminance – it's different), etc.
People with abnormal colour vision will have different equiluminance points.
Anstis SM, Cavanagh P (1983) A minimum motion technique for judging equiluminance. In: Sharpe Mollon JD, Sharpe LT (eds) Colour vision: Physiology and psychophysics. London: Academic Press: 66–77 [PDF]
Raphael S, MacLeod DIA (2011) Mesopic luminance assessed with minimum motion photometry. Journal of Vision, 11(9):14, 1–21