Most often IPv6 ready means that the webservers have been configured to support IPv6 only traffic. Test a page loads from a IPv6 only connection, or use tools like Alexey R. suggested.
If the code was changed for this IPv6 support, maybe you need to test more. Do a risk assessment with the one whomever implemented the change.
My guess would be that if you can reach the site yourthen you are done, any other testing sounds overkill. But if you do not know what IPv6 is, maybe read up on it first before you make an decision.
