When water is placed in a balloon, the balloon can be placed over a flame without popping. Water absorbs the heat from the flame, so the rubber of the balloon does not become weak and break like it does with the dry balloon.
When the bill is dipped in the water/alcohol mixture then lit on fire, the water protects the bill from burning. A large amount of the alcohol is vaporized from the heat causing a large flame around the bill.
C2H5OH + 3O2 → 2CO2 + 3H2O