Browns are carbon heavy organic materials like straw, fall leaves, shredded paper etc (see https://www.helpfulgardener.com/forum/viewtopic.php?t=9089) as opposed to "greens," the nitrogen heavy stuff like grass, coffee grounds, manure, etc. So you can see it is not about color.
The browns absorb odors, keep the pile from getting too wet, provide food for the micro-organisms that help the composting process and also feed the soil, break down slower, so keep the composting process steadier (like time-release medications). Browns help keep the organic nitrogen from escaping and aid in producing humus, so that your end product becomes humus rather than just broken down grass. Helps make sure your compost finished product is well balanced, has good tilth, and contains all the necessary nutrients.
I always cover greens with browns in my compost pile. I use them about 50 / 50 by volume, but it doesn't have to be exact. In winter when I have lots of fall leaves and fewer weeds, the pile tends to be more brown. In summer when the fall leaves are mostly used up and there's lots of weeds, it tends to be more green, but it works both ways.
Here's a composting 101 article: