Question: what do the symbols under pokemon mean?
Answer: Those symbols are set only by players and is completely up to the player. There are coincidentally 6 marks (equal to the number of stats: HP, Atk, Def, Sp. ... Def, Spd) you can 'mark' or un-'mark', which can be ideal to mark what stats of a Pokemon are at 31 IVs, which I've found to be the most common use of these.