In gray box testing, test engineer is equipped with the knowledge of system and designs test cases or test data based on system knowledge.
For example, consider a hypothetical case wherein you have to test a web application. Functionality of this web application is very simple, you just need to enter your personal details like email and field of interest on the web form and submit this form. Server will get this details, and based on the field of interest pick some articles and mail it to the given email. Email validation is happening at the client side using Java Scripts.