The four schools of Sunni Islam are each named after a classical jurist (who had no idea his rulings would be so imitated - the concept of taqlid, "blind imitation", arose later on).
The Sunni schools are the Shafi'i (Malaysia), Hanafi (Indian subcontinent, West Africa, Egypt), Maliki (North Africa and West Africa), and Hanbali (Arabia).
These four schools share most of their rulings (80%?) but differ on the particular hadiths they accept as authentically given by Muhammad and the weight they give to analogy or reason (qiyas) in deciding difficulties.
The Jaferi school (Iran and Iraq) is more associated with Shia Islam. The fatwas, or time and space bound rulings of early jurists, are taken rather more seriously in this school, due to the more hierarchical structure of Shia Islam, which is ruled by the imams. But they are also more flexible, in that the imams have considerable power to consider the context of a decision, which has been lacking in Sunni Islam historically.
Each school reflects a unique al-urf or culture, that being the one that the classical jurists themselves lived in, when rulings were made. Some suggest that the discipline of isnah which developed to validate hadith made it relatively easy to record and validate also the rulings of jurists, making them far easier to imitate (taqlid) than to challenge in new contexts. The effect is, the schools have been more or less frozen for centuries, and reflect a culture that simply no longer exists.
Early shariah had a much more flexible character, and many modern Muslim scholars believe that it should be renewed, and the classical jurists should lose their special status. This would require formulating a new fiqh suitable for the modern world, e.g. as proposed by advocates of the Islamization of knowledge, and would deal with the modern context.
This modernization is opposed by most ulema who spend much time memorizing the traditional schools of classical jurists, and who typically lack the power or infrastructure to research or to reliably enforce rulings that go beyond the traditional norms. They often accuse those who seek to reform fiqh of seeking simply to replace Islam with a more secular form of democracy and law.
See also: shariah, qiyas, hadith, al-urf, taqlid, ijtihad