Cross-field matching is a term in the DemandTools Dedupe module which describes the action of matching values across different fields on a single object. It increases the likelihood of finding a duplicate record.
You are searching for duplicate contact records using the Dedupe module. You decide that if the contact's home phone numbers match, then those records are likely duplicates.
But, if the home phone number on a contact record was entered by accident into the business phone number field and you tried to match records on the home phone number, a match would not be found.
With cross-field matching, you can look for a match in both the home and business phone number fields.
So in our example, if a contact's business phone number matched another record's home phone number, then by your rules those records are likely duplicates.