What chemical is made when baking soda and vinegar mix?

As an overview, acetic acid (HC2H3O2 (or C2H4O2 in solution), from the vinegar) reacts with aqueous sodium bicarbonate (NaHCO3), forming sodium acetate (NaC2H3O2) and carbonic acid (H2CO3). As also happens in carbonated water, the carbonic acid then dissociates into water and carbon dioxide (H2O and CO2). The chemical reaction would be (not balanced):

C2H4O2 + NaHCO3 --initial reaction--> NaC2H3O2 + H2CO3 --bubbling--> NaC2H3O2 + H2O + CO2