Fiqh is arabic for comprehend or understand. To make reason out of the Qur'an and Hadeeth and draw the laws and way of life that govern Muslims.

Washing for prayers is considered Fiqh science, which in part is drawn from the Qur'an and hadeeth.

There are 4 major schools of fiqh in Islam today:

Imam Mohammed Ibn Abdul Wahab.
Imam Al-Shafi'e.
Imam Al-Hanbali.
Imam Al-Hanafi.

Abdul Wahab is the most orthodox, mainly practiced in the Arabian peninsula and Afghanistan.

Al-shafi'e, Hanbali and Hanafi are mainly practiced in Egypt and other parts of the Muslim world. The differences between each school can hardly be noticed, one can think of each school as revivals to the old laws. There have been many schools through out the centuries rising and falling. Abdul Wahab revived the Arabian peninsula back into old Islamic laws after seeing people associate worshiping trees and grave yards of dead people with Allah.