They, as their names imply, are a group of anthropomorphic penguins who appear in the animated sequence. Each one wears a black bowtie
Three of them are cheerful, but their leader appears cynical.
They are seen in the animated sequence when Mary Poppins and Bert, specifically during the part where the song "Jolly Holiday" pauses for a bit and then resumes. They serve them and enjoy a dance with Bert. Later, he offers Mary to dance with them just as they join him and Bert. They are not seen again for the rest of the film afterward.
They serve people at the Ink and Paint Club in this film. Eddie Valiant orders a scotch on the rocks from one and adds, "And I mean ice!" The penguin returns with his drink with a diamond in it ("ice" is a slang term for "diamond"), upon which he replies, "Toons." Two of them appear at the end of the film alongside the other cartoon characters.
A different group of penguins wearing the same bowties from Mary Poppins makes an appearance in the episode Save the Whale. They are a group of performing penguins that perform in Pettigrew's Penguin Park. When they feel like they want to escape it just like Spot, Ariel, Flounder, and Sebastian, they manage to do so along with Spot.
In this film, they remain a point of contention between P.L. Travers and Walt Disney, as Travers is adamant about refusing to have them in Mary Poppins since it feels they would dumb down her books. When Travers cries at the premiere, is it ambiguous whether she's sad about them being left in Mary Poppins (as she claimed both in this film and in real life) or about how Mary Poppins reminds her of the tragic relationship with her father.
In the sequel, they make a reappearance still in an animated sequence at the Royal Doulton Bowl where all the inhabitants are anthropomorphic animals. They dance along with Mary and a cast of animals during the song "A Cover is Not the Book". They look somewhat different from their original versions as they are heavily redesigned with larger eyes, more distinct appearances from one another, and a more elaborate costume (their bowties being supplemented by hats and evening wear) — casting doubt on whether they are the same ones as their original version, although they certainly appear to know Mary.