What determines the color of a hen's egg?

It's just genetics. Some hens lay white eggs and some lay brown eggs.

It's interesting that you asked this question because less than a month ago I was in a local store that sells free range eggs out of a refrigerator in the back of the store and, when I opened the packs to check them out I found a mix of white and brown eggs in the same container which caused me to ask this question as well.

The color of eggs has little to do with taste. It also has little to do with how a chicken looks. Some people believe that white hens lay white eggs, for example. That may be true but it may not. I was told, however, that a hen has an "earlobe" whose color will give away the color of egg that hen will lay. A white earlobe would yield a white egg a hen whose earlobe is more red will lay a brown egg.

Great question.

The color difference is due to the specific breed of hen,
Hens with white feathers and white earlobes lay white eggs,
whereas hens with red feathers and matching-colored earlobes lay brown eggs.
White Leghorn chickens are white and lay white eggs
Rhode Island Red and New Hampshire chickens are reddish brown and lay brown or brown-speckled eggs.

Woow, thanks!