The answer depends on which database you use:
SQLite - The data is contained in a file in the App_Data directory, so when you copy the files to the server, you copy the data, too. This is the easiest way to move a gallery and its data.
SQL Server - The data is stored in SQL Server, which can be stored anywhere, but it is often stored on the web server. When you move a gallery, you have to migrate the database, too, and possibly update the connection string in web.config. If you are not comfortable with SQL Server, consider sticking with SQLite or spending some time "getting to know" SQL Server.
Roger Martin
Creator and Lead Developer of Gallery Server Pro