Tails are crucial cellular sensors. Depending upon type, cell cilia can sense fluid movement, chemicals, osmotic pressure, temperature, and/or gravity.
Mammalian adaptive immune system T-cells have no apparent cilium, but they do have the equivalent. The synapse that activates a T-cell acts like a cilium and is built much the same.
Cilia are critical to intercellular communication. In animals, they help maintain organ function via continuous feedback loops. In epithelial tissues, the cilia of host cells may actively recruit microbial symbionts.
The asymmetry of human bodies is established within a few hours after an embryo begins developing. This is done by the tails of cells sweeping clockwise, generating a net leftward flow, which tells left from right, and determines situs solitus: the position of organs.
Damaged tails often spell cell death. If the cilia of cells cannot function, disorders arise. Badly behaved or non-functioning cell tails are instrumental in many diseases.