Stars are resources that can be collected and accumulated in order to fill up the gauges that allow you to win designs and to receive a gift at the end of a level.
They are collected at the end of a successful level. You earn one star for each word found in the level's word list, and you can earn an extra star by filling the bonus word gauge.
To collect even more stars, you can watch an ad (on the end-of-level screen) by clicking on the "Star x2" button to get double the number of stars obtained during the level.