A replying party application is a web application that relies on an ADFS server to authenticate an user's identity. In other words, it relies on the ADFS server's claim for authentication. In order for an ADFS server to support a web application, you need to add the web application as a Relying Party Application in the Relying Party Trust. Of cause, the preamble is that the web application is a Claim-Aware application. How to make an web application claim aware is beyond the scope of this document.