Think of 'appendage' as a smaller physical part that visibly connects to a bigger object. A tail is an appendage of some animals.
Pro Tip 2/3
Not Always Essential
'Appendage' often suggests the part is not essential for the main object to function. Fins are appendages that help a fish but aren't crucial for survival.
Pro Tip 3/3
Metaphorical Use
The word can be used metaphorically to refer to things that aren't physically connected. The outdoor patio acts as an appendage to the café.