A reporting log contains all the information required to generate a specific report, including its reporting prompts. A reporting log record is created each time a report is run with a unique set of reporting prompts.
Reporting logs are used to enable Chatter. See Setting up Chatter for more information. The Chatter feed for a report is maintained however many times a report with the same prompts is re-run.
The Reporting Logs object has a tab and also appears as a related list on the Reporting Definitions page layout.
You can run the report from the Reporting Log related list by clicking the name of the reporting log.