In the professional kitchen, "brunoise" is a specification for a fine dice knife cut. Specifically, if you are told to brunoise something, it means that the item should be cut into 1/8" cubes. Common vegetables that you would brunoise include but are certainly not limited to shallots, onions, carrots, and celery.
To get to brunoise size it is best to form your food item into a rectangular block or tranch and then from there cut 1/8 planks. Then, Take each plank and cut 1/8 inch batons. Once the entire item has been planed and then batoned, the batons can then grouped and cut into brunoise.
Other dice specifications include large dice - 3/4" by 3.4", medium dice - 1/2" by 1/2", and small dice - 1/4" by 1/4". Mince and "chop" are not the same as dice.