What is Azure:
Azure Services Platform (Azure) is an internet-scale cloud services platform hosted in Microsoft data centers, which provides an operating system and a set of developer services that can be used individually or together. Azure’s flexible and interoperable platform can be used to build new applications to run from the cloud or enhance existing applications with cloud-based capabilities.
How Services platform look like:
Per the article, it will be like
How it's used with Exchange:
Microsoft also offers cloud applications ready for consumption by customers such as Windows Live, Microsoft Dynamics, and other Microsoft Online Services for business such as Microsoft Exchange Online and SharePoint Online. Due to Azure's open architecture which gives developers the choice to build web applications, applications running on connected devices, PCs, servers, or hybrid solutions offering the best of online and on-premises.
How Exchange is getting "Cloud ready":
Regarding this, quite some time earlier I found this wonderful article at channel9, presented by Jason Henderson, Senior Lead Program Manager for Exchange Web Services team. The new Exchange Web Services Managed API provides managed code access to Exchange, whether running on premises or in the cloud. Learn how this new Microsoft .NET API provides full access to Microsoft Exchange mail, calendaring, scheduling, contacts, eventing, synchronization, permissioning, and public folders programmatically using the Exchange Web Services protocol.
If you haven't attended PDC ’08 in L.A. at the last October (2008) you can watch the Exchange Web Services Managed API: Unified Communications Development for Exchange session. This will be the first time that the API has been shown in public.