A petrodollar is a US dollar received by an oil producer usually deposited into Western institutions. After the collapse of the gold standard, US Secretary of State, Henry Kissinger, and the Saudi Royal family made the following agreement: oil was to be sold ONLY in USD (making the USD the reserve currency) and in return USA was to offer military protection to Saudi Arabia. Also the Saudis should invest their surplus in US debt securities. In 1974 the petrodollar system was fully operational and 1 year later the rest of oil producers joined the system.
The rest of non-oil-producing countries favored cheap exports to the US to get dollars they will spend on oil (like Japan). The petrodollar system increased demand for USD and US debt securities.
If the main export of a country is oil and it is going to be priced in USD, the natural solution for the oil producer is to peg its currency to USD. It has happend with the Saudi Riyal (SAR), Azerbaijani New Manat (AZN) or Kazakhstani Tenge (KZT). However, with the recent low prices of oil, the tension to keep the peg to a strong dollar is unsustainable. So far AZN and KZT have broken it:
Just to give a hint, last year AZN devalued 50% and KZT initially less (August 2015), but later the rest until the same 50%.
Now the big question: what is going to happen with the Saudi Riyal? As a rule of thumb, Saudi has an annual deficit of 100B USD (which could increase or decrease -less subsudies, VAT...) and foreign reserves of more than 500B. So, they can resist for a while (IMF thinks only 5 years). But they can extend the number of years of resistance by selling Aramco (biggest oil company in the world). Let say it is worth 1T, and they sell 40% of the company, so 4 more years with deficits of 100B. Do we really think they are going to see their reserves evaporating? Probably no. Taking into account that 50% of the population works for the public sector, therefore being paid in SAR, and the need to arm themselves to be prepared to continue to war against Yemen and probably other surrounded countries, they might break the peg with the US dollar after Aramco's IPO.
The consequences of this break are huge. Probably starting with Turkey and the devaluation of TRY and continuing with the Malaysian ringgit, and so on.