[Update:] There seems to be some confusion about how zakkokumai is cooked and looks like, so I've added some more photos and such.
Rice is such an integral part of a Japanese meal, that the word for 'meal' (gohan, ご飯) also means rice. White rice is the norm, both for taste and for various cultural reasons. But as you probably know, white rice (hakumai, 白米） is rice that has been stripped of most of its nutrients, leaving just the starch.
Brown rice (genmai) is the obvious healthier alternative. But brown rice can take some time to cook, what with the soaking and so on that's needed, and some people simply don't like the taste or texture.
In recent years, something called zakkoku-mai (雑穀米）has become increasingly popular in Japan. Zakkoku just means "mixed grains", and mai is rice. Another name for essentially the same thing is kokumotsu gohan （穀物ご飯）.