Finance can cover any of the processes and procedures required to collect, store, distribute, or account for the convention's money. The convention needs income to buy things, and the money has to stay somewhere before it is used, usually a bank account. The process of making it clear the money was not wasted (or stolen), an audit, is supported by careful record-keeping and saving receipts.
At a minimum, someone must be granted the authority to collect, store, and distribute the funds of the convention. Typically this person is called the Treasurer. Physical property and other assets must be accounted for as well. One or more persons should be designated to audit the bookkeeping from time to time and report back to the Executive Committee.
A Budget should be created and approved, and then actual expenses should be tracked.