what are differences between classic mode and claim based authentication in SharePoint 2010
Classic mode authentication: This is nothing but windows authentication. It means it will work based on you windows logged in credentials. There is a problem in classic mode authentication. Once a site is created under this authentication then Form based authentication can not be configured on the site.
Claim based authentication: Claim based authentication provides you a way to implement form based authentication as well as windows authentication. It is built on Security Assertion Markup Language (SAML) and Windows Identity Foundation.