Oh man, this is intense. I'll do my best to keep it clear and concise. This is specific to the current situation - the Saudi/Iran rift has been going on for decades, and I'm not adding personal speculations about Yemen / oil / outside factors. Thanks for the request, @donnie !
  1. There are two main factions of Islam.
    Sunni (majority of Saudi) and Shia (majority of Iran) Islam. The differences stem from who should have succeeded (politically and theologically) the Prophet Muhammed. There are some doctrinal differences / holidays for different martyrs / weight is put on certain aspects of faith differently. To me, it seems similar to the Catholic/Protestant divide.
  2. Separation of church and state is not a thing.
    Laws and governing in the Middle East* are intrinsically tied to Islam (sharia law). Religion is very political. HOWEVER there is still a mix of Sunni and Shia in every country. (Sunni is more prevalent almost everywhere except Iran, where Shia is the majority.)
  3. Saudi executed a prominent Shia cleric.
    Sheikh Nimr al-Nimr was executed along with 46 others, mostly convicted al-Qaeda members, on Saturday. He was charged** with political dissidence and incitement.
  4. Al-Nimr had strong ties to Iran.
    Not only was he a big deal in the Shia community, but he had studied theology in Iran for over a decade. Iran has repeatedly condemned/lobbied against his arrest, trial, and sentencing.
  5. Iranians reacted to the execution with violence.
    The Saudi embassy in Tehran was burned, as was the consulate in Mashhad. There were reports of protesters burning the Saudi flag in the streets. Iran issued a statement condemning the execution... But also condemning the violence, and has arrested many of the protesters.
  6. Saudi pulls out of Iran.
    Saudi issues a statement condemning Iran, pulls out government officials, stops flights to Iran, urges businesses to stop trade, and issues a travel ban for Saudi citizens. NOTE: Saudi is still allowing Iranian pilgrims to enter Mecca for Hajj at this time.
  7. Other gulf countries follow suit.
    Be it the GCC or Sunni-ruling majority - Kuwait, Qatar, and Bahrain*** have removed their ambassadors / are expelling their Iranian ambassadors. UAE has downgraded their Iranian ambassador to "charge d'affaires."
  8. Ban Ki-Moon condemns everybody.
    This is my only personal political view I'll share. All the Secretary General of the UN does is condemn people. He condemns like three countries a week. Does this do anything tangible? No. Is this useful? No. But, whatever, you're all condemned.
  9. The end?
    This situation is kinda at a stalemate. Keep your eye on Yemen in the next few days - I expect the violence there to ramp up. Please feel free to ask me questions in the comments; I'd love to clarify/do more research and get back to you! (And fact-check the hell out of me, please.)
  10. A note on executions
    Saudi is the third leading country for executions, after China and the US - but Iran has still executed over 400 people in the past year, mostly Kurds.
  11. Footnotes
    * Lebanon's government does a Sunni/Shia/Christian balance in political office. ** From my reading, I have not found confirmation that al-Nimr was involved with "terrorist activity," but reports are all very polarized right now. *** BAHRAIN is a great example of a Sunni ruling party and a vocal Shia minority - why you'll see Bahrainis protesting al-Nimr's execution BUT the country severing ties with Iran.