Bismillahi Al-Rahmani Al-Rahim
The title "amir al-mu'minin" with respect to hadith is the highest and most esteemed rank. It applies to someone who has reached the furthest limits in hadith, including: memory, skill, knowledge of the disciplines associated with hadith, and knowing their subtle defects. This is the type of person the jurists, judges, and hadith masters turn to. The list of scholars to achieve this rank are few. Some of the early Imams given the title amir al-mu'minin include: Sufyan al-Thauri, Shu`bah bin al-Hajjaj, Hammad bin Salamah, `Abd Allah bin al-Mubarak, Ahmad bin Hanbal, Al-Bukhari, Muslim. Ibn Hajr al-`Asqaline is one of the later scholars given the title amir al-mu'minin. (See Dr. Nur al-Din `Itr, Minhaj al-naqd `end al-`ulama', p77)
Basically: This is someone who has memorized all there is to memorize, and who knows everything that is known - about hadith, that is.
And Allah knows best.
Wa al-salamu `alaykum,