>>49920733A mark is a thing that goes in the ribbon section of a pokemon's summary. It cannot be acquired by doing something, pokemon just have a chance of having one when they spawn, an Uncommon Mark is like 1/50 and a Rare Mark is about 1/100. Those are just rue vanilla marks, there are marks like the curry mark that pokemon you get by making curry have a chance of having, marks that pokemon who spawn in cold climates can have and so on, there's even a super special mark that hasn't been used yet, presumably it's for special event pokemom but so far none of those have come with it.
Basically dont worry about it, it's for collectors and autists since unlike balltism and shinies, other people will never see it