Windows Azure Diagnostics enables you to collect diagnostic data from an application running in Windows Azure. You can use diagnostic data for debugging and troubleshooting, measuring performance, monitoring resource usage, traffic analysis and capacity planning, and auditing. After the diagnostic data is collected it can be transferred to a Windows Azure storage account for persistence. Transfers can either be scheduled or on-demand.
My colleague, Greg Oliver, describes how to do your diagnostics in a blog post entitled, Windows Azure Diagnostics–From the Ground Up.