A distributed ledger keeps track of all your transactions, but it's not a master file—it is maintained in different locations for security purposes.
With the cloud, you can think of your distributed ledger kind of like a shared online document (Google, Microsoft, etc.) that multiple people can access. There's no need for a centralized master file to check against malicious edits, and the contents are protected via encryption with limited access. Because it's distributed across various locations, a distributed ledger is harder to attack, so it's more secure.