We've written about ACABAR de before -- because it's such a useful combination. When you place a de after acabar, it takes on the meaning of, to have just. ACABAR by itself means to end, to end-up, to finish. I've noticed that so many of you are getting these two forms mixed-up (confundida).
A few examples should help clear this up:
You see the difference now?
That de makes a big difference.
Now, listen to some examples in context.