The Big Mac Index compares the price of the same product — a Big Mac — in different countries, converted at the current exchange rate. If, once converted, the sandwich is cheaper in a given country than in the United States, that country's currency is said to be undervalued.
The underlying idea is serious: it is purchasing power parity. The method, for its part, is deliberately rough and ready, and the newspaper says so. It has nonetheless survived forty years, spawned an academic literature — the term burgernomics — and provided one of the few economic indicators that everyone understands.