If you look up close to your standard mirror, you will see two reflections from the mirror. One from the reflective coating behind the layer of glass - the mirror image, and the second fainter reflection from the surface of the glass. This is known as ghost images

A front surface mirror eliminates this second reflection by having the reflective coating on the front surface of the glass. Hence it gives a better, clearer image of the reflected object when at close range, instead of a reflected object with its faint double image.

Why is this important to me?
Because the dental mirror is always held in close proximity to the tooth. Very close proximity. Take root canal therapy - when looking for the orifices to the root canals, it is very distracting to have double images moving around. These things are so bloody small it ain't funny. Also applies to precision margins during a crown preparation procedure (the infamous "crown prep") on a tooth.

How do you tell the difference?
Take a pencil, or use your finger, and use it to touch the mirror. Look at the reflected pencil- is it touching the real pencil? If it is a standard mirror, there will be a distance between the two, and this distance is equal to the thickness of the glass. Aka back surface mirror or second surface mirror.

With a front surface mirror, the reflected pencil image will be touching the real pencil. Unfortunately for me, the coating on these mirrors also scratches more easily than the surface of glass.

And there's a catch.
Any front surface mirror on a wall is probably (definitely) not designed to be just an ordinary mirror with up-close benefits. It's a see-through mirror, aka two-way mirror, though not exactly accurate in its nomenclature. For observation by a another party behind the glass. Also applies to sun-glasses.

Creepy! Go check your public bathroom next time. Does your finger touch it's reflection???