Ursula's Garden

Ursula's garden is her collection of merfolk that hang around the entrance hall to her lair. Each one was once a mermaid/merman who came to Ursula for help in some matter, but couldn't afford her high demands, leaving them helpless before her power.

The Little Mermaid
The polyp's first appearance in the movie was when Ursula chuckled at the idea of Ariel becoming a, "charming addition to my little garden."

Their second appearance was when Ariel went to Ursula's lair. Ariel was disgusted by the sight of the polyps, but continued forwards anyways. One of the polyps grabbed Ariel's wrist and tried pulling her away from Ursula's lair, but in a fit of fright, Ariel managed to pull her wrist away.

During the song, Poor Unfortunate Souls, Ursula explained the backstory of how all her polyps were merfolk who were unable to pay her price, so she took them as compensation, and if Ariel was unable to complete her side of the deal, she would be transformed along with them.

During the battle with Ursula, King Triton was transformed into a polyp when he decided to take Ariel's place in the deal, but shortly after the battle, (when Ursula was killed), he and the rest of the garden were transformed back into merfolk.

Trivia

 * Despite what many may think, the polyps weren't an original concept by Disney. They were taken from the original fairy tale, only there they were guardians to the witch's lair instead of damned merfolk.