In bluetooth pairing is the first step in connecting two bluetooth devices. This step is to establish permission that the two devices can communicate with each other. For BTunes this is when you first use it with a device such as a smartphone. You will need to set the BTunes to pairing mode, and then select it on the smartphone's bluetooth menu in order to establish the two as paired devices, that is they are allowed to communicate with each other through bluetooth. This only needs to be done once with each device unless you wish to unpair the devices later.
Connection is the step after pairing, this is the state of the BTunes actively communicating with the device it has previously paired with. When you turn on BTunes it will automatically connect with paired devices that have their bluetooth turned on. Once BTunes is connected to another device the LED on the BTunes will flash twice in intervals. While BTunes is connected it can play audio streamed through the other device.
Disconnecting is stopping the BTunes from communicating with a connected device. You can disconnect BTunes by turning it off, turning off the bluetooth of the connected device, or go to the connected device's bluetooth menu go to the BTunes and select disconnect (this option can be seen by hitting the i next to BTunes in iOS or the gear symbol for Android. Once disconnected the BTunes LED will change from flashing twice in intervals to flashing only once in intervals.
You can reconnect to BTunes by going to the bluetooth options in your device and clicking on the BTunes entry under paired devices. Alternatively, pressing the multifunction button once while BTunes is disconnected will cause it to try to connect to the nearest paired device that has bluetooth turned on.