There is a conventional classification of essentially, four blood types known as the ABO system. These are namely A, B, AB and O blood types, discovered by Karl Landsteiner in Vienna in the early 1900's, whilst trying to figure out why blood transfusions saved lives and at times, were in fact the reason why death would occur. These blood types are relative to human beings as well as primates.
To understand the ABO system, it is first important to know the definition of an allele. An allele is an alternative form of a gene. Each person inherits two alleles for each gene, one allele from each parent. These alleles may be the same or may be different from each other.
A, B and O are alleles. We each inherit one type of allele from each parent to make a gene. There are six possible combinations for these three alleles: AA, BB, OO, AB, AO, and BO. These pairs of alleles can therefore be referred to as the "genotype" for blood group of that particular person or primate. For knowledge's sake, a genotype can be defined as a specific pair of alleles that an individual possesses at a certain location in the genome.
To keep it simple, the following pair of alleles an individual inherits from both parents will produce the following classification of blood group i.e.: phenotype (The characteristics, in this case blood group, manifested by the individual);
AA= Blood group A individual
BB= Blood group B individual
OO= Blood group O individual
AB= Blood group AB individual
AO= Blood group A individual
BO= Blood group B individual.
As you can observe from above, individuals with AO and BO alleles will manifest not blood group O but of A or B phenotypes (Blood groups). This is because alleles A and B are "dominant" and when together (as in AB blood group individuals) they are "co-dominant". Blood group O on the other hand is recessive, and therefore despite being present in the genotype, will not be manifested in the phenotype.
Individuals of the O blood group have two recessive alleles. These individuals to safely donate blood to any of the six combinations of blood grouped individuals, allowing them to be "universal donors". On the other hand, these individuals can only accept type O blood themselves.
Individuals of type AB, are consequently "Universal receivers" allowing them to safely receive blood from individuals of any blood type, but they are unable to donate blood to any other blood type.