Vinegar (acetic acid) is an acid, while baking soda (sodium bicarbonate) is a base. When mixed they first undergo a neutralization reaction to give sodium acetete and carbonic acid. The unstable carbonic acid then decomposes into carbon dioxide and water. The carbon dioxide produced is responsible for the bubbling observed.
Vinegar (HC2H3O2) combined with baking soda (NaHCO3) produce carbon dioxide gas, water, and aqueous sodium acetate, NaC2H3O2. Physical observations include agressive bubbles of gas and a decrease in temperature.