Here's the chemical reaction:
NaHCO3 (baking soda) + CH3COOH (vinegar) → CO2 (carbon dioxide) + H2O (water) + CH3COONa (sodium acetate)
This reaction is a classic example of an acid-base reaction. The vinegar acts as an acid, and the baking soda acts as a base. The reaction releases carbon dioxide gas, which is what causes the fizzing and bubbling you see when you mix these two ingredients.