Baking soda is scientifically known as “sodium bicarbonate” or, if you lived a century or more ago – bicarbonate of soda.
The chemical formula for baking soda is NaHCO3, where Na is the sodium ion, and HCO3 is the bicarbonate ion. CO3 is also known as the carbonate ion, so another acceptable name is “sodium hydrogen carbonate”, though it isn’t preferred because it simply takes too long to write/say.
Baking soda generally behaves as a weak base in water. This means that it will react with a strong acid to make a salt and a weak acid.
As an example, take hydrochloric acid (found in your stomach).
HCl + NaHCO3 -> NaCl + H2CO3
The products are sodium chloride (table salt) and carbonic acid.
In fact, every reaction of baking soda and an acid in water produces the same carbonic acid. This is important, because carbonic acid breaks down in water in a reversible reaction to make water and carbon dioxide.
H2CO3 -> H2O + CO2
Carbon dioxide is soluble in water, up to a point, but if you produce more than can stay in solution, the rest comes out as bubbles – the fizz you know from all carbonated beverages (carbonated refers to the carbonate ion, if you hadn’t guessed).
Those carbon dioxide bubbles are also the driving force in the classic vinegar and baking soda volcano. Vinegar is dilute acetic acid, and when they react, the carbon dioxide bubbles surge upwards, carrying the liquid with them in a gloriously messy eruption, leaving sodium acetate (the salt from this reaction) coating everything.
CH3COOH (acetic acid) + NaHCO3 -> H2CO3 + CH3COONa (sodium acetate)
Sodium bicarbonate can also behave as a weak acid, when exposed to strong bases. In this case, water and a weak base are formed. This generally isn’t a very useful process however, because then carbon dioxide dissolves into the solution from the air, forming carbonic acid, which then reacts with the weak base to reform the bicarbonate.