Final answer:
The word 'obsequious' means attentive in an ingratiating or servile manner. It refers to the waiter's behavior in the given context.
Step-by-step explanation:
The word 'obsequious' means attentive in an ingratiating or servile manner.
In the given context, it refers to the waiter who is overly attentive and trying to please the person.
The waiter's obsequious behavior is shown by his constant presence behind the person's chair and the perpetual grin on his face.