Published by a financial magazine since 1986, the index takes a product made to a similar specification worldwide and compares local prices at market exchange rates. It is a teaching device for purchasing-power-parity rather than a model, and it is deliberately presented as such.
Its flaws are the interesting part. A burger is mostly non-tradable inputs, rent and local wages, so poorer countries look systematically cheap. Adjusting for income per head removes a lot of that bias and changes several rankings.
It does capture extremes. Currencies that look 40% or 50% cheap on the index are usually ones where a story about weak growth, high inflation or capital flight has been running for years.
Example: a burger costs $5.80 in the US and ¥480 in Japan, implying 480 / 5.80 = 82.8 yen per dollar. With the market near 150, the index puts the yen roughly 45% below its burger-implied level.
Related: purchasing-power-parity, law-of-one-price, real-exchange-rate, ninja