The idea that identical items in different countries should have the same "real" prices is very intuitively appealing- after all, it stands to reason that a consumer should be able to sell an item in one country, exchange the money received for the item for currency of a different country, and then buy the same item back in the other country (and not have any money left over), if for no other reason than this scenario simply puts the consumer back exactly where she started. This concept, known as purchasing-power parity (and sometimes referred to as PPP), is simply the theory that the amount of purchasing power that a consumer has doesn't depend on what currency she is making purchases with.
Purchasing-power parity doesn't mean that nominal exchange rates are equal to 1, or even that nominal exchange rates are constant. A quick look at an online finance site shows, for example, that a US dollar can buy about 80 Japanese yen (at the time of writing), and this can vary pretty widely over time. Instead, the theory of purchasing-power parity implies that there is an interaction between nominal prices and nominal exchange rates so that, for example, items in the US that sell for one dollar would sell for 80 yen in Japan today, and this ratio would change in tandem with the nominal exchange rate. In other words, purchasing-power parity states that the real exchange rate is always equal to 1, i.e. that one item purchased domestically can be exchanged for one foreign item.
Despite its intuitive appeal, purchasing-power parity doesn't generally hold in practice. This is because purchasing-power parity relies on the presence of arbitrage opportunities- opportunities to risklessly and costlessly buy items at a low price in one place and sell them at a higher price in another- to bring prices together in different countries. (Prices would converge because the buying activity would push prices in one country up and the selling activity would push prices in the other country down.) In reality, there are various transaction costs and barriers to trade that limit the ability to make prices converge via market forces. For example, it's unclear how one would exploit arbitrage opportunities for services across different geographies, since it's often difficult, if not impossible, to transport services costlessly from one place to another.
Nevertheless, purchasing-power parity is an important concept to consider as a baseline theoretical scenario, and, even though purchasing-power parity might not hold perfectly in practice, the intuition behind it does, in fact, place practical limits on how much real prices can diverge across countries.
(If you are interested in reading more, see here for another discussion on purchasing-power parity.)