Bombs appear when you form a seven or longer Chain by erasing Tsum Tsum. Tap a Bomb to detonate it and erase the Tsum Tsum around it. Outside of normal Bombs, some will also increase the number of Coins you get or even add play time.
-Bombs in normal missions
Coin Bombs = +10 coins
Time Bombs = +2 sec. play time
-Bombs in Co-op/Battles
Healing Bombs = +100 HP
Binding Bombs = Paralyze the enemy for a few seconds
Critical Bombs = Deals more damage than normal ones
There are other special Bombs available through skills.