The aim of Catch a Falling Star is just that - to catch falling stars and score points. The game mechanic is very simple - you simply move your basket left or right in order to catch the stars. At the same time, you must avoid hazards, like ice, which slows you down, for example. Various power-ups and power-downs will help or hinder you on your path to your best score yet.
Your basket fills up as you catch stars, and only once you deposit them on either side of the screen do you score the points. Depositing when your basket is full gives you bonus points, but the risks are higher, since missing a star makes you lose any stars you haven't deposited yet.
Source: The Game Website.