The Big Mac index was invented in 1986 by the magazine The Economist, and considers the Big Mac hamburger sold in McDonald’s as its basket of reference. This index is based on the purchasing power parity theory. When analysing exchange rates through this theory, we compare an homogeneous basket of goods (a Big Mac) available in the analysed countries.
Since Big Macs are sold all around the world and can be considered to be homogeneous, it allows us to make simple calculations. For example, if the price of a Big Mac in the US is $1.2 and in Brussels €1, the exchange rate should be 0.83 euros per dollar. By dividing the domestic currency price in each country by the price in dollars, we can calculate the purchasing-power parity, and comparing it with the current exchange rates test whether the currency is under or overvalued.
The results are not exact because there are other factors that influence them, for instance, the local preferences of the consumers. However, they give a reasonable approximation with a very simple calculation.
More on the Big Mac index in The Economist website.