This experiment was to match white light by adding three other wavelengths. This group made an interesting applet https://graphics.stanford.edu/courses/cs178-10/applets/colormatching.html
Why was he trying to match white/gray light specifically? Intuitively we know that white light is a combination of all the wavelengths of light, but how did he know that back in the day?
To julialuo: From https://royalsocietypublishing.org/doi/full/10.1098/rsta.2007.2178: This was discovered by Newton from 1665–1666 when he passed sunlight though a high quality prism and found that white light was split up into the colors of the spectrum, and when he passed through a second prism, the light was not split up into any further colours. Maxwell in the 1800's used white from Newton's work in the area of color theory.
To answer the above question, there was already an intuition in the fact that color was made of three bases, and that mixing them together would be produced by spinning the wheel. So, basically, the inside of the wheel was used to create a gray color that would match with the gray color created by the colors, and vice versa, to try and find what combination of each of the three bases was needed.
Also, here is the link in the slide