baking soda (sodium bicarbonate) + vinegar (acetic acid) --> carbon dioxide + water + sodium ion + acetate ion
NaHCO3(s) + CH3COOH(l) --> CO2(g) + H2O(l) + Na+(aq) + CH3COO-(aq)
where s = solid, l = liquid, g = gas, aq = aqueous or in solution
Breaking it down:
NaHCO3 <--> Na+(aq) + HCO3-(aq)
CH3COOH <--> H+(aq) + CH3COO-(aq)
H+ + HCO3- <--> H2CO3 (carbonic acid)
H2CO3 <--> H2O + CO2
Acetic acid (a weak acid) reacts with and neutralizes sodium bicarbonate (a base). The carbon dioxide that is given off is a gas. Carbon dioxide is responsible for the fizzing and bubbling during the 'eruption'.

