A general appearance usually means your are there for all purposes and do not contest whether the court has jurisdiction over you.
The opposite is a special or limited appearance. For example, if you live in Texas and have no connections with State A except that your spouse goes to State A to file for divorce, you could make a special or limited appearance to inform the State A court that you are not subject to State A personal jurisdiction. So, your spouse could get a divorce that would only end the marriage due to State A having in rem jurisdiction, but State A could not divide your money because it lacks personal (in personam) jurisdiction over you.
Likewise, both the Uniform Child Custody Jurisdiction Enforcement Act (UCCJEA) and the Uniform Interstate Family Support Act (UIFSA), have provisions that a person can make a limited appearance to contest custody/visitation, or contest support, yet be protected from litigating other matters.
You only get one shot at appearances, etc. and it is a very thin line that is easily crossed. One needs to raise jurisdictional/appearance issues before answering a divorce complaint. The answer could constitute a general appearance.
This is likely one of those situations that if you ask whether it is important, it probably is important. Even if it turns out not to be important, it is worth having an attorney address your particular circumstances.
