What is Al Jarh Wa at-Ta'dil ( الجرح و التعديل )? and what is it's purpose?
It is part of Hadith sciences and anytime you read a classification of a Hadith someone has made checks on the narrators etc. (one known having done that is Imam Hanbal for example).
A narrator must be righteous/upright and accurate (in memory or in writing)... any narrator lacking in one or both of these areas is considered having deficiency as a narrator.
Which means that one has to check a narrator for anything that might discredit him/her like being known to have a poor memory or to lie etc. If such deficiency than it is stated , and this is known as Al Jarh. Al Jarh is stating a deficiency in the narrators righteousness or accurateness.
This involves trying to find out facts about his/her behavior etc. in respect of the above mentioned aspects (righteousness/accuracy).
Saying something bad about a person which is not present is considered backbiting and is a severe sin.
But this is done not to hurt others, but to keep safe the Deen of Islam.
The above is a short summary of these 2 sources:
Ajarhu Wa Ata'deel ( الجرح و التعديل ) is a science of the sciences of Hadith, dealing with identifying the narrators whether they are reliable or not. Ajarh/الجرح is finding a deficiency whether it is in his righteousness (عدالته) or in his accurateness (ضبطه), or in both. Of the deficiency is in his righteousness then the Hadith would fall under Mawdu' (موضوع) and Matrook (متروك). If the deficiency is in his accurateness, then the Hadith will fall under Da'eef, Munkar, Mttarab (مضطرب), Mushaf, Maqloob, and Mudraj (المدرج).
Atta'deel, is describing the narrator in His righteousness and accurateness with what is required for accepting his narration. The acceptance of the narration would fall under, Hadith Mutawatir, Saheeh, Hasan, and their types.
It's purpose is to keep Islam safe. Ajarh Wa Atta'deel is Fardh Kifayah, which means it is required only on some not all, Fardh Ayn means it is required on all Muslim.
Sources: Manzoomat fi Qawa'id Ajarhu wa Ata'deel منظومة في قواعد الجرح و التعديل, Kitabul Ilal lilimam Ahmad , Muqadima fi Ajarhu Wa Ata'deel كتاب العلل للإمام أحمد -مقدمة في الجرح و التعديل, Qawa'id Ajarhu Wa Atta'deel (قواعد الجرح و التعديل)