This simply means that you've done all the work that you were given for the day.
However, it can also mean that you were given too much work and you can do no more. In which case, you would say, "I'm done for the day." This could mean things like "I can do no more" or "I'm done-in" - things that mean that I can't do anymore. I'm too tired or simply can't go on.
If you said the second case, you'd be going home early - unable to do more. I think it mostly means the first example. You've done your work and are finished for the day.
Rich