Given the balanced equation representing a reaction: H2SO3 + H2O « H3O+ + HSO3-
According to one acid-base theory, the H2SO3 molecules act as (AKS 5g)

An acid because they donate H^+ ions

Explanation:

Let us look at the equation again;

H2SO3 + H2O « H3O+ + HSO3-

An acid donates hydrogen ion while a base accepts hydrogen ion. Hence, we have to look at which species that acted as hydrogen ion donors or acceptors.

We can clearly see that H2SO3 acted as a hydrogen ion donor while H2O acted as a hydrogen ion acceptor.

Thus, H2SO3  acted as an acid by donating hydrogen ions.