Appearance – This is the actual presence of a person in a court hearing. Either as a claimant, defendant, accused or any other party, which participates in a civil or criminal court case. It provides that this person accepts the power of the court to try the matter (i.e. “jurisdiction”). Sometimes, depending on the local process rules, participants in the court process can make a limited participation called a “special appearance”. There their presence is not to imply acceptance of the court’s jurisdiction. But, rather, to challenge the jurisdiction of the court. An example of the usefulness of a “special appearance” would be where a person wants to state the fact that they have been never properly notified with the court documentation. So they didn’t have the time to prepare for the hearings and to protect their interests.
Lawyers are usually the people who make appearances on behalf of their clients. So then any appearance by a hired lawyer on the case binds the client, who participates in it.
Note that lawyers do not practice law for free; their personal advocacy is paid. So when asking a lawyer for their appearance on a concrete legal dispute in court hall, you should pay them for their opinion and legal advice/representation; it is the same like when you visit a doctor and pay for their competent diagnose and accurate medical treatment.