I don't need to be dropped off

Firstly, on the meaning of dropping off someone or something, from the Cambridge dictionary

drop off something/someone

phrasal verb with drop verb

to take someone or something, esp. by car, to a particular place:

I’m about to leave – can I drop you off somewhere on my way home?

Secondly, on its usage in the context of the question:

Since you cannot use your car while it is being serviced, some people may expect that the dealership will drop you off somewhere (and maybe come and pick you up later and bring you back to the dealership, when the service is completed).

This question is an indirect way of telling you that they will not do that. It indicates that your only two options are that you will find your own way to wherever you wish to go while waiting for the car to be serviced, or you'll just wait at the dealership. It is indirect because it doesn't just say "We do not provide dropoff services for customers while their car is being serviced". Instead, it

• doesn't list dropping you off somewhere as an option
• explicitly lists not dropping you off as an option ("I don't need to be dropped off")