A “consultation” is a meeting that involves gaining information, discussing issues, and/or seeking advice. With a consultation there will be an information exchange and back-and-forth conversation in some form. A consultation can happen in person, online, on the telephone, or (less commonly) via email exchanges. An “initial consultation” simply refers to the first consultation you have and it is almost always the first step in engaging the services of a professional, including a lawyer.
Most of the time, an initial consultation with a lawyer will last for at least one hour. The lawyer you meet with will talk with you about the issues that have brought you to them and will try to give you various options and scenarios with regard to retaining their services. They should be able to give you some idea of what you can expect from your professional relationship going forward, including with respect to steps you may wish to consider taking, how complex your problem is or may become, and the cost associated with different courses of action you may take.