Fiqh means the practices and rulings of Islam deducted by Islamic scholars from Quran and Hadith, the 2 primary sources of guidance. The need for systematization of Islamic knowledge such as Fiqh (practices and rulings) and other sciences such as ilm al hadith (sciences of hadith), Tasawwuf (science of spirituality) and all related subjects came to be developed later due the need of time.
During the Prophet's life, his example was right in front of the companions and whenever verses of Quran were revealed they were direct witnesses to it. Therefore the companions had direct access and first hand experience of the revelation process and its implementation unlike Muslims of the later centuries. They not only witnessed but also recorded them. Additionally they were a smaller community, concentrated in to one large group within the 2 major cities of Islam i.e. Makkah and Madinah. If any companion erred or forgot about a particular practice or ruling of the Prophet ﷺ, he was immediately corrected by the other who was living within the same community. After the passing away of the Prophet ﷺ, gradually Islam spread throughout the region and it accepted new people in to its fold. When new people entered Islam especially during the Rashidun period i.e. during rule of first 4 successors of Prophet Muhammad ﷺ (namely Abu Bakr (r.a), Umar (r.a), Uthman (r.a) and Ali (r.a)) the companions also spread to different regions. There they focused on the preservation of knowledge they had learned from the Prophet ﷺ and focused on teaching to the local people. This is how schools of thought came to be developed in early Islam that were named after each companions such as school of Abdullah ibn Masud (r.a) in Kufa and Abdullah ibn Umar (r.a) in Makkah, Abu Darda (r.a) in Damascus, Muadh bin Jabal (r.a) in Palestine and other companions went other places. Therefore, the people of each town had their own set of teachings they acquired from them and were satisfied.
Later on these cities were exposed to the hadith and sunnah information of the Prophet ﷺ which was taught in other cities by other companions which led towards the developing stage of various sciences such as ilm al hadith (sciences of hadith), fiqh (rulings and practices) and better understanding of Shariah (Islamic law). This also caused the need for pious among the knowledgeable to learn more by travelling to those cities which they did and compiled books and knowledge, and taught there, which then led towards development of major schools of thoughts such as 4 (Maliki, Sha'afi, Hanbali, Hanafi) and subsequent systematic compilations of hadith books. Many of these scholars that hailed from each major city of the Islamic world were all students of the teachers who themselves were students of either those learned from the Tabi'een (second generation or students of companions) or lived longer to have claimed learning directly from the companions. Therefore this is a process of traditional knowledge which has been handed down from the time of Prophet ﷺ to later generations through medium of pious and knowledgeable ones in a systematized manner.