BluetoothMate and Lilypad board
I am having a hard time answering your questions because of a few reasons:


I don't know your history
I don't use a Mac
I have never used the BluetoothMate or Lilypads


With that said, I am going to take a stab to see if I can help.

Bluetooth modules like the BluetoothMate tunnel serial just like FTDI USB chips do. This means that you can write serial on one end and it shows up on the other end just like if you had a serial cable connected to your computer.

With a PC, you would power on the bluetooth module, then from the PC search for the bluetooth module. After connecting, Windows adds a virtual COM port that can be accessed through a terminal such as PuTTY.

On Unix based systems, I believe I remember it being a device such as /dev/ttyUSB0.

Hopefully this helps some.