In Marxian political economy, exchange value refers to one of three major aspects of a commodity, i.e., an item or service produced for, and sold on, the market. In simple terms, the exchange value of a commodity is nothing but its price.
The three aspects of the commodity can be seen in the following quote from Marx's Capital:
This first part says that the value of commodities as they are exchanged for each other - or when stated in terms of money units, their prices - are very different from their value in use to human beings, their use-value.
Next, Marx describes how had abstracted from the differences in use-value and thus from the concrete differences amongst commodities, looking for their shared characteristics. He famously found that what's left is that all commodities have value (or "labor-value"), the socially necessary abstract labor time needed to produce it. That is, all commodities are products of labor, as part of the community, with each commodity producer contributing his or her time to the societal division of labor. Each commodity is social in its nature.
Third, value is not the same thing as exchange-value (or price). Rather, the value is the shared characteristic of the exchange-values of all the commodities. He calls this the common factor, whereas someone else might call it the essence. In contrast, the exchange-value represents the appearance or "form" of value. Just as with used cars, the shiny appearance may differ radically from the lemony essence. In fact, one of his major themes (the theory of commodity fetishism) is that the system of commodity exchange that dominates capitalism obscures the class nature of that institution.
To Marx, the "exchange value" of a commodity represents its owner's purchasing power, the ability to command labor, i.e., the the amount of socially necessary abstract labor time that can be purchased using it.
In volumes I and II of Capital, Marx usually assumed that exchange values (and prices) were proportional to value.