Why are cilia and flagella important to unicellular organisms?

Cilia and flagella are found in most unicellular organisms, as well as in multicellular animals.

In unicellular organisms, they serve as the only means by which the organism can move itself around, other than simply following the natural currents of whatever medium they live in. Cilia are a large number of tiny strands, while flagella are a small number of larger (well, less-tiny) strands; but they both serve the same basic function, agitating the surrounding medium (usually water) to effectively "swim" through it in a particular direction, thereby improving access to nutrients or avoiding predators. In multicellular organisms (such as us) they also often take on many different functions, but in unicellular organisms they're almost always for locomotion.

Bacterial flagella actually function like propellers, spinning around in a screwlike motion to propel water backward. Eukaryotic flagella (such as those on human sperm) function differently, beating back and forth in a complex swimming motion.