When you've added another Claims Provider Trust to ADFS, next to ADFS, you'll see the HomeRealmDiscovery page when you try to logon. This page looks like this:
Most users don't know what to select here. So you wouldn't want them to see this page.
You can add a setting to your application web.config which tells adfs to use a specific Claims Provider. This setting is called homeRealm. The value can be found in Adfs Management tool.
homeRealm="[Claims provider identifier]" />