In the update 0.69.0 (android) and 1.39.0 (iOS) one of the items on the release notes is:
Added icons to the Pokémon information screen to indicate how the Pokémon was caught.
Where can I see these icons, and what do they represent?
According to this article, the caught icons represent whether you caught your Pokémon via normal methods, as a raid Pokémon, or via hatching an egg:
Other minor features include new icons that show how the Pokemon was caught — this will let you see if you caught the Pokemon via a Raid Battle, while exploring, or via an egg.
As the update is now out for iOS, here are what these icons looks like:
For a Pokémon caught in a pokéball:
For a Pokémon caught in a great ball:
For a Pokémon caught in an ultra ball:
For a Pokémon caught as a raid boss (since all raid Pokémon must be captured in premier balls):
As indicated by Wondercricket in the comments below, Pokémon hatched prior to this update just have the pokéball icon, instead of some sort of egg icon:
However, Pokémon hatched after the update do have egg icons: