In a system
XC6H4GY this is conjugation involving the substituent
X, the benzene ring and the side-chain connective-plus-reaction site
GY, i.e. either
X is a
+R group and
GY is a
-R group, or
X is a
-R group and
GY is a
+R group. In Hammett correlations this situation can lead to the need to apply exalted substituent constants σ + or σ-, respectively, as in electrophilic or nucleophilic aromatic substitution, respectively. The term 'through resonance' is synonymous. Cross conjugation has also been used to describe the interactions occurring in 2-phenylallyl and similar systems.
Source:
PAC, 1994, 66, 1077. 'Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)' on page 1101 (https://doi.org/10.1351/pac199466051077)