What distinguishes Maliki jurisprudence is a claim about evidence. Malik ibn Anas taught in Medina, the city where the Prophet lived and was buried, and he held that the settled practice of its people, amal ahl al-Madina, was itself proof of the sunna. If the whole community of the city did something continuously, that continuity was better evidence of what the Prophet had done than a single chain of transmission running back through one narrator who might have misremembered.
The Muwatta is the book that shows the method working. It is arranged by legal topic and moves between prophetic hadith, the reported opinions of Companions and their successors, and plain statements of what the people of Medina do, without treating the last of these as the weakest. That is why it is read as both a hadith collection and a law book, and why it is among the earliest surviving works of either kind.
The argument against the principle was made early and has never gone away. Al-Shafii, who had studied with Malik, objected that the custom of a city is a local habit and cannot outrank an authenticated report of what the Prophet said. The Maliki reply distinguishes practice transmitted continuously from the generation of the Prophet himself, which carries the weight, from later Medinan usage, which does not. The dispute is one of the clearest cases in Islamic law of two schools disagreeing not about a ruling but about what is allowed to count as a reason for one.
Sources The Canonization of Islamic Law: A Social and Intellectual HistoryAhmed El Shamsy with Principles of Islamic JurisprudenceMohammad Hashim Kamali