Mouthpiece and Ligature
Here the tone is created. The mouthpiece is usually made of hard rubber (ebonite) or plastic, but sometimes also of Glass, Crystal and Metal. The reed is fixed onto the mouthpiece with a ligature that uses screws.
Barrel
Usually the instrument comes with one of these but space in the case for another - usually one that is a little longer and one that is a little shorter. These are used to fine tune the instrument and to adapt it to the player and the orchestra's pitch.
Upper Joint
This part of the body holds the keys for the Left Hand.
Lower Joint
This part of the body holds the keys for the Right Hand. The Upper and Lower Joints could be made from 1 piece but having them separate makes cleaning and transport much easier.
Bridge Key
One of the first lessons taught the beginning clarinet player is how to put the clarinet together and take it apart without bending the bridge keys. These are the keys which bridge the key system from the upper to lower joints. One key on the upper joint rides above the companion key on the lower joint. The thing to watch is that the key on the upper joint is lifted so when the two joints are pushed together the bridge keys do not snag each other and become bent.
See the photo below for a close up!
Bell
Contrary to popular belief, the bell does not amplify the sound; rather, it improves the uniformity of the instrument's tone for the lowest notes in each register. For the other notes the sound is produced almost entirely at the tone holes and the bell is irrelevant.