An audit trail is a log of actions taken in a system: who logged in, who changed a price, who approved a payment, and at what time. Each entry is kept as a record in its own right, so that the history can be checked later rather than reconstructed from memory.
It matters most when something goes wrong or someone asks questions. If a customer disputes a quote, you can see who edited it and when. If a buyer or auditor reviews your business, a clear trail shows that decisions were made in an orderly way. It also discourages careless changes, because people know their actions are recorded.