It means that the heart was beating very fast. You can say that something is racing when it is moving or going very fast. Other examples: - He raced down the street (= he ran/went very fast down the street) - The car raced by the spectators (= the car went very fast by the spectators) Of course, a heart doesn't move, but it has a movement -- it beats! That's what the sentence means.

It is more dramatic to say "my heart was racing". It is more descriptive than "I was so anxious or I was so nervous that my heart was beating very fast". Hope that helps!