When person marries someone, he/she has the option to terminate their relation by asking for Divorce.
Divorce just as marriage, can be of many types. The other type that my fellow brother has told you are not of 2 types, they are one!
However generally the terms that are well-known can be categorized under:
Just the way, a person marries a girl by having people to know about their relation. Some witness are/must be there! Paper work must be done in order to keep a record and to go for a legal act to let the female get/ask for her rights to her in-laws.
Try taking an example of a newly married girl, she might get a baby soon. If she is divorced, what would you expect her to do? That is why Nikah was signed in between both of the parties (boy and girl). Now she can ask for her Haq Meh'r and other rights, such as food and shelter for her/her in-laws baby etc.
In Islam, a woman completes her iddat in her husbands house (if husband is alive). So that if she has to be pregnant it would be taken a note there.
Even after the divorce, that has taken place such as (husband has said 'I divorce you' three times) there is a trial period for 3 months for husband to retry to maintain their relation. In this period, they can be wife/husband again without any issue.
Also, remember the divorce that took place in aggression is never accepted since that was an emotional divorce and would be not a good decision for both of the families. That is why, the trial period of 3 months has been given to the families.
In our cultures, we people aggressively take our daughters back to our home saying, 'Lets go daughter! These people don't deserve you'. Well if they didn't why you married her to them in the first place?
Also, I would like to beg a differ to other answer. There is no such thing as
The triple Talaq ends the marriage permentantly and you cannot marry the same woman again until she marries again, consummates the marriage and the marriage ends.
In Islam it is not allowed, this is just a ritual made up by ourself. You will not be able to find any of the example of Halaala (this ritual is known as Halaala; in which a divorced girl is married to someone else and she has to go through sexual intercourse with that guy, and then upon a divorce from him, she can marry the first person again. Huh!). That's why, that answer is not fully supported and is based on a ritual rather than the true teachings of Islam.
A female or male, can go to court and ask for divorce legally, if she/he has any sort of trouble. Wife can ask for her rights too, like to keep the children in her own custody, to ask for monthly payment by male for her and her children's expenses.
You can learn more about the Legal divorces here: