What the checks cover
An IBAN is a two-letter country code, two check digits and a country-specific account part of fixed length. Validation confirms the country is known, the total length is right for that country, and the check digits are consistent with the rest of the number under the ISO 7064 mod 97-10 algorithm. That checksum catches all single-character errors and almost all transpositions, which is most of what goes wrong when a person types an IBAN.
Check digits of 00, 01 and 99 can never be produced by the algorithm, so they are rejected before the checksum runs. It is a small rule, and a surprising number of validators omit it.