Accounting software is a program that can run on a computer to track the total value of a company. Accounting software can be downloaded to a computer or can be used through a browser window by logging into a website.
Before computers all accounting information was stored in books called "ledgers". A general ledger was the book where the accountant wrote down all payments that came into a company and all payments that were made. A common term for keeping track of this information is called "keeping the books". A bookkeeper is another term for an accountant, but can sometimes means a person who does accounting but maybe doesn't have as much formal education as an accountant.