What is the name of the long, thin structure that propels certain unicellular organisms?

The long, thin structure that propels certain unicellular organisms is known as a flagellum. Flagella are whip-like appendages that extend from the cell body and enable movement through liquid environments by rotating or undulating. This structure is particularly important in many aquatic unicellular organisms, such as certain protozoa and bacteria, where mobility is essential for accessing nutrients or escaping predators.

In contrast to cilia, which are shorter and typically cover the entire surface of a cell and beat in a coordinated manner to create movement or fluid flow, flagella tend to be longer and often work independently. Pseudopods are temporary projections of the cell membrane used by some cells for movement and feeding, particularly in amoebas, while indentation does not refer to any biological structure related to movement. Therefore, the flagellum is specifically adapted for propulsion, making it the correct answer in this context.