This common idiomatic expression means ‘quickly and continuously’ and is often used in talking about money. For example:
“What a busy day. We took in money hand over fist. They were buying things hand over fist.
“In the current economic crises, many companies are losing money hand over fist.”
This expression is probably naval in origin referring to the movement one makes when pulling rope. Originally it meant slow progress, as when two ships were pulled together by ropes but today it has come to mean with great speed.
Your fist is your hand with the fingers closed tightly.