The "butterfly man" was a tall, yellow-skinned, insectoid bipedal creature encountered in a pocket universe by the Thirteenth Doctor. Although not reminiscent of a butterfly himself, he was known as such due to collecting individuals of interest and displaying them behind glass like prized butterflies.
When the Doctor went to find Yaz in the pocket universe, she eventually discovered that the butterfly man had bought her from Salonius' Slave Store and shortly met him carrying Yaz in a glass pod into his base. She later found he had killed and displayed many unknown aliens as butterflies, but managed to recover Trip and used him to find Yaz, who was already escaping with other survivors.
When the Doctor opened portals back to the main universe, the butterfly man was one of many who tried to stop her, but he eventually returned to his own time and place. (COMIC: Hydra's Gate)