It's the rarity/tier of the pokemon. If I remember correctly:
circle=t1
diamond=t2
star=t3
yellow star=t4
rainbow = t5
It's an indicator for how much stats and AP/PP they have. They also get different effects from steroid items btw: t1 gets +10, t2 gets +7, t3 gets +5, t4 gets +2 and t5 maybe +1?
