A daily bonus is effectively a small gift you get every day starting from Level 8. When you log into the game for the first time during the day, you'll see a window with 9 shells. Select one of them to get a random booster, like a Diving Glove, a Hammer, Two Bombs, etc. During in-game events, bonus shells might also contain event currency or fuel for your bathyscaphe.
IMPORTANT NOTE: you need an internet connection to claim your daily bonus!