Mincing or dicing means to cut into very small pieces. The easiest way to mince or dice a piece of fruit, vegetable, or meat is to make long, thin rod-like pieces, then to cut them horizontally. The term “minced” means to create even smaller pieces than diced, but the technique is typically the same.
Recipes that call for vegetables such as carrots, celery, and leeks to be cut into small, even pieces generally describe them as diced rather than minced because it’s so tough to get them into the truly tiny pieces that “minced” connotes. When you want onion or garlic in a dish and don’t want them to be apparent, you want to mince them as small as possible.
Here is an example of how to dice vegetables, in this case, a leek. Making long thin strips and then turning them horizontally to cut them into tiny pieces creates dice.