You can provide a host address that includes the path to a specific folder on the remote host. CuteFTP Mac considers the path "relative" by default.
For example: If you log into FTP server ftp.myserver.com as user joeuser, the initial remote folder will be the home folder for that user (e.g., /home/joeuser). If you want your Documents folder inside your home folder to be the initial remote folder, you enter the host address as ftp://ftp.myserver.com/Documents. This connects you directly to home/joeuser/Documents.
You can also specify an absolute path by adding an extra slash: ftp://ftp.myserver.com//some/absolute/path. For example, if your default home folder is users/home/joeuser, but you want to open a connection to users/Documents, you would specify ftp://ftp.myserver.com//users/Documents.