Hive Dollars and Steem Dollars are both forms of debt on their respective chains. They mostly come from the normal issuance of tokens (author rewards and funds for the DAO are paid out as Hive/Steem Dollars). The printing of these debt tokens increases during a bull market because the rate at which they are created is based on the price of Hive/Steem.
I recently wrote a post explaining Hive Dollars. You can also check the explanation in the original Steem whitepaper.
The initial HF away from steem?
This is not the main source, but Hive did elect to carry over the debt at the time of the fork. We did not have to, and other Steem forks such as Blurt did not. In my view carrying over the debt is a sign of legitimacy of Hive as continuation of Steem project.