A cross-appeal arises when one party appeals a lower-court decision and the opposing party also asks the appellate court to change part of that decision. The first filing is usually called the appeal, while the other party's request for a different outcome is the cross-appeal. Both can be considered together.
Imagine a company appeals a finding that it broke antitrust law. The government might separately cross-appeal because it believes the remedies are too limited. The company could be seeking to overturn liability while the government seeks a stronger remedy. These are distinct requests even though they arise from the same case.
Responding to an appeal is not necessarily a cross-appeal. A party can argue that the judgment should be affirmed without asking the appellate court to change it. In US federal civil cases, the rules provide an additional filing window for other parties after the first notice of appeal, but precise deadlines and procedures depend on the case.
When following litigation, check who filed each notice, which parts of the judgment each side challenges and whether the appeals have been decided. A cross-appeal means the court has been asked to revisit an issue, not that the original ruling has already changed.