A cross-connection is any connection between the water supply and a source of potential contamination. This could be from a faulty plumbing fixture, pool, storage tank, that when used, might enter the drinking water supply.
An example would be to use a hose to clean a grease arrestor, if there is a sudden drop in water pressure (e.g. due to a water mains break) this could siphon the contaminated water into your water pipes and therefore, the drinking water supply.