Integrated application pool mode
When an application pool is in Integrated mode, you can take advantage of the integrated request-processing architecture of IIS and ASP.NET. When a worker process in an application pool receives a request, the request passes through an ordered list of events. Each event calls the necessary native and managed modules to process portions of the request and to generate the response.
There are several benefits to running application pools in Integrated mode. First the request-processing models of IIS and ASP.NET are integrated into a unified process model. This model eliminates steps that were previously duplicated in IIS and ASP.NET, such as authentication. Additionally, Integrated mode enables the availability of managed features to all content types.
Classic application pool mode
When an application pool is in Classic mode, IIS 7.0 handles requests as in IIS 6.0 worker process isolation mode. ASP.NET requests first go through native processing steps in IIS and are then routed to Aspnet_isapi.dll for processing of managed code in the managed runtime. Finally, the request is routed back through IIS to send the response.
This separation of the IIS and ASP.NET request-processing models results in duplication of some processing steps, such as authentication and authorization. Additionally, managed code features, such as forms authentication, are only available to ASP.NET applications or applications for which you have script mapped all requests to be handled by aspnet_isapi.dll.
Be sure to test your existing applications for compatibility in Integrated mode before upgrading a production environment to IIS 7.0 and assigning applications to application pools in Integrated mode. You should only add an application to an application pool in Classic mode if the application fails to work in Integrated mode. For example, your application might rely on an authentication token passed from IIS to the managed runtime, and, due to the new architecture in IIS 7.0, the process breaks your application.
Taken from: What is the difference between DefaultAppPool and Classic .NET AppPool in IIS7?
Original source: Introduction to IIS Architecture