All players of Pokémon Go will start seeing sponsored gifts popping up in the game, bringing a sponsored message and a gift to anyone who opens one. These 'gifts' will appear after spinning a Photo Disc at a Pokéstop or Gym, or after a Raid battle, and will show the logo and name of the sponsor before giving you an option to open it up.
As for what these contain, they will bring a sponsored message and gifts, and will allow players to read further into a sponsored offer should they be interested. Players will never have to read into the offers however, if they choose to decline the gifts, and there is a limit as to how many gifts a player can receive a day.
While this does seem to showcase another way for Niantic to generate revenue for its popular AR mobile game, it is seemingly done in a way that isn't as intrusive as the pop-up ads most free-to-play mobile games feature. Niantic has mentioned in the post that announced these gifts that players can choose to opt-out of sponsored gifts, a setting that will not affect how players receive gifts from other sources.
Likewise, child accounts will never receive sponsored gifts, even if the account in question has sponsored gifts enabled via the Niantic Kids Parent Portal or the Pokémon Trainer Club Website.