GamePress
Date Stamp on Pokemon
Report
Answers
As part of the last update it's given to Pokemon that are a minimum of one calendar year old. Today is 11/29/2018 (or 29/11/2018 if you're European), so any Pokemon that were caught on 11/29/2017 or older will bear a stamp. Pokemon caught on 11/30/2017 or more recent will not bear the stamp until the calendar rolls over them.
It's a QoL update that lets people see at a glance which Pokemon are old for trading purposes. In addition, the date of the Pokemon's capture is shown in the trade synopsis screen where it lists the CP and HP ranges before pressing confirm.