Alright, i'll give you a situation here.
Let's say that you're breeding for a bagon with perfect IV's in attack and speed. You breed 200 bagons and finally get the one you're looking for. In order to clear your box for more useful pokemon that you'll get in the future, you decide to release all the bagons you don't need. You mark the bagon that you want to keep, and then release the rest. Then, when you see the mark, you'll know not to release that bagon.
Basically, marks make a pokemon unique when compared with other versions of the same pokemon when those pokemon are in a box.