A cross-appeal is a request filed by an appellee requesting that a higher court review a decision made by a lower court. The difference between an appeal and a cross-appeal is essentially arbitrary and dependent only on who filed the request for a higher court's review first. The first party to file is called the petitioner or appellant, and its request for review is an appeal. If an opposing party (called the respondent or appellee) also wishes to request review of a lower court's decision, that request is called a cross-appeal.
It may be helpful to think of these terms' equivalents in civil trials. In a civil trial action, the plaintiff files a claim against the defendant. If the defendant has claims agianst the plaintiff, it may file a counterclaim. Again, the terminology is arbitrary and dependent only on which party filed its complaint or request first.
Note that no cross-appeal exists when an appellee simply wishes to have a lower court's decision upheld by a higher court, just as no counterclaim exists where a trial defendant simply wishes to deny the plaintiff's claims without making any of its own. A cross-appeal occurs only if the appellee requests that the higher court review some aspect of the lower court's decision, and not to simply uphold the lower court's decision.
See civil procedure