Most of the time a sentence that looks like this is used, it means the same thing as:
I will finish it by tomorrow.
For instance: imagine your teacher asks when you are going to turn in an essay. If you say "I will have it done by tomorrow.", he will not think you are hiring someone else to do your homework!
This is a bit strange. Because usually when you speak about "having something done", you mean someone else will be doing it for youat your direction. For some reason, "I will have it done by (time)" came to mean "I will finish it by (time)" anyway.
The phrasingIt may have originally developed from wanting to emphasize "one way or another, it will be finished--no matter what it takes!" to an authority; Not identifying who will be doing something makes things sound otherworldly and thatfirm, think of: "It will be done." So perhaps wanting to sound firm is why it's the authority doesn't needresponse to worrybeing asked about howsomething you accomplish italone are responsible for (like homework).
Still, in certain contexts it actually does mean:
It will be done--by someone who is not me--and I will ensure this happens before tomorrow.
For instance:
"I told you to hire some workers to come in here and fix the hole in the wall. When is that going to happen?"
"I will have it done by tomorrow."
So you have to look at context to know what the meaning is supposed to be.
Notice that if you say "I will have it done by April" that could either mean you will be doing it by the month of April, or you will be hiring someone named April to do it. :-)