Despite the lack of conclusive scientific proof, a person's blood type is an indication of their personality, temperament, and hence their compatibility with other people. Many Japanese, especially those who read women's magazines and watch morning TV shows, consider it for interpersonal relationships.
People with type A blood are friendly and kind; with type B are spontaneous and creative; with type O are confident and aggressive. Those with type AB are a mix of type A and B traits.
Believers might be comforted with the knowledge that their partner's blood type is compatible with there's, but the superstition can have unfortunate consequences by misjudging people or even descriminating against them.
As a foreigner living in Japan, people have been astonished when I tell them I've no idea what my blood type is. The superstition in Japan is as strong, if not stronger, than the use of astrological signs.
And as with astrology, there are an infinite number factors other than blood type which determine our personality, temperament and compatibility with other people.