There isn't an exact definition to "Minced" like there is for Julienne or Brunoise it is a more loosely defined cut. Garlic, Ginger and many spices are minced so their flavor will be distributed more evenly throughout an mixture. Also the mincing process releases oils and flavors that really only come out through that process.
I am mincing Garlic here, it probably comes up the most often. First I cut the bottom off a Garlic clove then with the side of my French Knife I smash it to break it up a little, then the last bit of paper comes off pretty easily. After that, using a rocking motion with the French Knife I finely chop it up until it looks like it does above.