Cross-functional testing is verification of non-functional requirements.
These requirements are such characteristics of system that cannot be implemented like a normal feature.
Eg. Number of concurrent users supported by system, usability of site etc.
Cross-functional testing is related to cross-functional requirements.
Often business users do not specify cross-functional requirements in the beginning.
But they expect these when software is complete and deployed to production.
It is always a good idea to ask business users about such cross-functional expectations in initial phase of the project itself.
https://learning.oreilly.com/library/view/full-stack-testing/9781098108120/ch10.html