Avi is a Hebrew name, short of
Avraham (
Abraham). It is pronounced AH-vee (with the stress on the first syllable, as opposed to ah-VEE, which is a regular Hebrew word meaning "my father").
The similarity between the two is not incidental. The name
Avraham is explained in the bible as being "AV (father) + RAV (much, many) +
HAMON (crowd) = Father of a great number of people".
Those of you who have studied the Old Testament know that this was the name given to
AVRAM after God had made a covenant with him. His original name,
AVRAM meant "AV (father) +
RAM (high, dignified)".