It depends on how you configure it. From http://msdn.microsoft.com/en-us/library/ms998292.aspx and http://msdn.microsoft.com/en-us/library/bsz5788z.aspx ...
ASP.NET applications do not impersonate by default. As a result, when they use Windows authentication to connect to SQL Server, they use the Web application's process identity. With this approach, your front-end Web application authenticates and authorizes its users and then uses a trusted identity to access the database. The database trusts the application's identity and trusts the application to properly authenticate and authorize callers. This approach is referred to as the trusted subsystem model.
The alternative model referred to as the impersonation/delegation model uses the original caller's Windows identity to access the database. This approach requires that your ASP.NET application is configured to use impersonation. See the section "Impersonation / Delegation vs. Trusted Subsystem" in this document.
So depending on how you have configured it, it could use either the app pool account (not when not using impersonation) or the account of the logged-in user that is using the web application (when using impersonation).
See http://msdn.microsoft.com/en-us/library/134ec8tc.aspx for impersonation information.