Bismihi ta'ala
This topic has been addressed before, but very briefly, triple divorce means a husband uttering the divorce word ṭāliq three times, and the wife be irrevocably divorced.
The issue here is that in Islam, if a husband divorces a wife once, he can get back with her, and if it's a revocable (raj'i) divorce, he can do so during her 'iddah period. They can also get back together and remarry if divorce happens a second time, or after the 'iddah period.
However, on a third time, the husband cannot marry her again until she marries another man, and they consummates that marriage. Should the previous husband want her, she would then have to divorce this husband, observe 'iddah, and then remarry the previous husband.
This can be done only 3 times,which means on the ninth time, they can never marry again.
In some cultures, there are men who are employed to marry the divorced woman, consumate the marriage, and then divorce her so she can go back to her previous husband. They are called a muhallil (one who makes lawful".
In Shi'ah fiqh, this is all invalid and completely rejected.
In some Sunni circles, a triple divorce is invalid, and some are trying to reform this law.
In Shi'ah fiqh, there is no such thing as a triple divorce, and it will only be a single divorce, and that will only occur if all the conditions are met, and they are:
1. Wife is to have gone through a menstrual cycle, and not have been intimate with husband since ending of cycle. This means that husband must wait until wife has a menstrual cycle, finishes from it, and then he can divorce. Husband cannot divorce wife if she is in purity and he has been intimate with her.
2. It is done in front of a minimum of two just, righteous, pious, God-revering men.
3. The formula of the wording be done in formal Arabic, with correct pronunciation.
4. This is done willingly, by choice, and not forced or without intention.
Should these conditions be observed, the divorce with occur, but only once.
And Allah knows best.