blood type is determined by the "alleles" that are inherited from the parents. alleles are possible types of a particular gene, in this case the blood type gene. there are three basic blood type alleles: a, b, and o. children have two alleles, one inherited from each parent. the possible combinations of the three alleles are oo, ao, bo, ab, aa, and bb. these allele combinations lead to a specific bloodtype for the child.
when basic blood type genetics are understood, then it becomes relatively easy to understand that it is not at all unusual for two parents with blood type b (or blood type a) to have children with blood type o.