At all times, stars give you a small boost of light.
If you have at least one star, simply click on the star icon on the top right of your screen or double tap anywhere on the screen to activate that boost.
Later, stars allow you to unlock new jellyfish or new abilities (up to 3 at the same time) giving you tactical advantages in your survival. Once selected in the combo slots, these abilities will trigger everytime you use a star.