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They are markings, and at base have no real purpose. As an IV breeder, however, they are very useful for marking which stats on a pokemon are maxed and which are not since there are 6 stats and 6 marks. That way, when I look at my boxes later, I can tell at a glance which are the ones with 4,5, or even the rare 6 perfect stat pokemon.

If you need to differentiate pokemon from others of the same species but don't want to nickname them all, that is what they are for.

Perfect stats requires a lot of breeding. Normally, a pokemon is guaranteed to inherit at least two Individual Values (the number between 0 and 31 that plays a role in slightly randomizing every pokemon's stats) for stats from the parents. An item called Destiny Knot, when held by one of the parents, guarantees that a total of 5 IVs will be passed down to the child, chosen randomly from both parents. Any pokemon captured from the Friend Safari is guaranteed to have at least 2 perfect stats. You can take pokemon to the pokemon judge in the same town where the friend safari is (he's in the pokemon center) and he will tell you a pokemon's overall potential and which stats are it's best stats (if he says multiple stats, that means they all share the same IV, and if he says "They can't be better" or something like that, that means those stats are maxed). So, you capture a female of the pokemon you want to breed and check it's stats, then find a compatible male that has different max stats (say the female has max HP and Def, and the male has max Atk and Speed), then breed them while one of them holds the destiny knot until you get a baby that has max HP, Atk, Def, and Speed, then breed it with something that has max Sp. Def until you finally get a baby that has maxed out HP, Atk, Def, Sp Def, and Speed. An everstone also helps here so that you get the right nature, since the pokemon that holds the everstone will pass down it's nature to baby.

It's a very laborious process, but once you have a few males with good stats that are in multiple egg groups, it get's much faster.

Also, keep in mind that "Perfect Stats" means perfect stats for that species. A Weavile will always be faster than a Slowbro, because every pokemon has base stats that determine the minimum and maximum for every stat. Perfect Stats just means that they will be at that maximum, however high that is in any stat for any given pokemon

On top of that, it is useful to use I have found a stat fixing item in conjunction with a destiny knot in the early breeding for 2-3 IV pokes. As this helps force an additional IV.