A companion boost is a special way of making a companion even stronger for a level. When boosted, the Companion requires fewer companion dots for its power to be activated, and more dots on the board are affected by it!
It takes six companion dots to activate a companion's special ability. However, if you boost your Companion, their ability will be activated with only four Companion Dots collected. (Boosting a Companion will require you to use three Tokens)