Bad news: They're going to hang her instead.
Jezebel has a synopsis of the story so far. Basically, though, it's just what it looks like; she shtupped a guy who wasn't her husband, and they're going to kill her for it. The only legal wrinkle, beyond that, is that she was later convicted of killing her husband -- apparently while she was in prison. Any number of countries, Texas not least among them, execute you for murder. In this case, though, there seems to be some judicial uneasiness about the murder conviction; it incurred only a 10-year sentence, which was later reduced to five for mere "complicity." So they're going to kill her for adultery.
Now, there are all sorts of things wrong with the story. You don't have to oppose the death penalty full-stop to think it is misapplied here. You don't have to be part of the Republican Party's anti-Shariah wing to think that this speaks badly for jurisprudence in the Islamic Republic. You needn't support free love to think that this is wrong, nor need you consider Iran's international reputation salvageable to hope that the judges here will try to salvage it.
All you really need is to remember that Lady Justice has a pair of scales, and that they're supposed to balance. Adultery is a bad thing -- God's Top Ten, after all -- but, Leviticus 20:10 notwithstanding, a punishment like this would have been over the top even under the bloodthirsty Christianism of Europe's religious wars. (Witches and heretics were fair game; adulteresses -- except in royal cases like Anne Boleyn and Catherine Howard -- much less so.) To modern eyes, there is no way that judicial murder balances adultery.
Of course, no sensible person accuses Iran of having modern eyes. Or justice. On the other hand, they do have one of our drones, and (maybe) the makings of a an atomic bomb.