Al-walaa' : be loyal to .
Al-baraa' : wash your hands from or become innocent from or leave something away.
in Islam conducts :
1- Be loyal to Allah (by obeying his orders of what to do and not do), and his Prophet Mohammed -peace upon him-, and his companions , plus his followers and Muslim brothers.
(by loving them, supporting them, aiding & helping them and backing them up).
2- Clear and innocent from Allah infidels , polytheists , and dissemblers.
(including all their characteristics and similarities and acts and opposing them, not helping them)
but in some cases if they were one's parents , you should accompany them in the life with good turn but without opposing God's Orders.
its significance in political : be a loyal to your Muslim leader or group leader . and the inverse is correct by disobeying him if he is conflicting with Allah clear orders.
'Abdullah Bin Umar wrote to `Abdul Malik bin Marwan, swearing allegiance to him: 'I swear allegiance to you in that I will listen and obey what is in accordance with the Laws of Allah and the Tradition of His Apostle as much as I can.' Reference : Sahih al-Bukhari 7272
its significance in Islam :
1- its within the context meaning of "no god but Allah" as you should not obey any one else but Allah .
2- its a mandatory in faith's "Iman's" requirements as you should not obey the non-believers.
3- its the building block where Muslims community raise upon it.(faithful men are brothers)
4- not performing the walaa' and the baraa' may means you are infidel (by obeying the disbelievers)
5- its importance is due to mentioning it many times in the Quran Holy book and the Tradition of His Apostle (Prophet Mohammed peace upon him).
6- it distinguish you between the faith and the infidelity .
as far as i know there is no interference between schools about above general clarifications .