Certificate Authorities cross-sign each other when they get married together.
When CA Y issues a certificate for CA Z, then any system who trusts Y will indirectly gain confidence in everything that Z issues, since, for any certificate X issued (signed) by Z, a system that trusts Y will build the chain Y→Z→X. Thus, this cross-certification represents an assertion from Y that basically says: "everything that Z signs is as good as if I, Y, had signed it myself".
If CA Z also issues a certificate for CA Y, then trust goes both ways. Every system that trusts either Y or Z will be able to validate certificates emitted by both. The two CA are now really one, at least as far as trust is concerned.
A divorce would require revoking both cross-certificates, or at least failing to issue new ones when the cross-certificates expire.
(In practice, this kind of things happens when a new CA is created but is "morally" a replacement for the old one; or when a merger occurs between two businesses and they try to fuse their internal computer systems together.)