That is an admission that there is enough evidence that if presented to the jury would lead to a conviction.
It takes its name from the Supreme Court case, North Carolina v Alford, 400 US 25 (1970).
I get the impression from watching the show that the judge is ethically obligated to reject the guilty plea if he is not conviced that the person is really guilty.
If the person walks out of the court and says that they are innocent it seems incumbent on the judge to reject the plea.
I hope the judge drags her back into court and makes her either change her plea or give a detailed description of the crimes to which she is pleading guilty; make her either spell it out or go to trial.
I was initially sypathetic to this woman. She seemed to have left her past behind and made partial amends by being a good mother and giving back to her community. But her behavior since her arrest convinced me that she's a self-righteous liar and hasn't changed at all. Throw the book at her.