I'm not finished.
If the person is referring to work or an activity then this is broadly equivalent to...
- I am not finished
- I have not yet finished
- I have not completed the work
- I still have something to do
- There is still effort required
- The task I'm working on is not complete
It could imply a desire to continue...
- I haven't finished my food so please don't take my plate
- I'm still speaking so please don't interrupt, keep giving me your attention
In the context of drama the character might be expressing that they are not defeated or not yet exhausted. Often they will appear to have lost or be close to exhaustion. So it could mean something like the following...
- I have not been defeated
- I will continue despite a set back or hardship
- I have more effort/argument to make
- I will return to get revenge
I'm not finished, I'm just getting started.
A common rhetorical expression (often in the context of a conflict) to say I have plenty more to say/do.
With regards to Passive Voice. I'm not sure it is purely Passive.
This article gives good reasoning to that effect.
Another diagnostic test, which can sometimes be useful, to see if the candidate word is an adjective, is to try to see if the candidate word can be modified by "too" or "very":
"I am very finished with the website for now".
Nah, that isn't convincing either. Compare to: "Tom is very tired".