The value of a currency can depreciate in relation to the value of other currencies or to another benchmark.
Currencies can have their value determined by the cost of a basket of consumer goods from one period to another, but this is really just a measure of inflation. Inflation (or “deflation”) is a subset of the appreciation/depreciation metric, but changes in the exchange rates between currencies are typically seen as the most relevant measure of a currency’s value.
When an asset loses its redemption value in relation to a standardized benchmark, it is said to depreciate. Depreciation is not a realized loss, but instead is a nominal calculation based on the current value relative to the benchmark. With currencies, there a few benchmarks against which their value is judged.
One would be a standardized basket of consumer goods, and the cost of buying the same goods in the same country at different times is a rubric for calculating inflation rates. Inflation is generally only used to measure the value of a currency in one country over time.
Inflation rates calculated for each country can be compared to one another, of course, and countries experiencing more inflation than others will probably try to slow it down. The most useful way to evaluate currency value is by looking at the exchange rate of currency pairs.
When it takes progressively more units of currency A to get one unit of currency B, it is either because currency A is depreciating or currency B is appreciating. Comparing these two to a third or fourth currency should reveal which one is appreciating or depreciating.
Currencies that have depreciated are said to be “weaker” than others. Weaker currencies will cause a country’s exports to appear more attractive to international importers, so it can be a good thing.
China and Japan actually have flooded the market with their own currencies and bought lots of US treasuries to keep their currencies from appreciating so that they can continue to benefit from the trade surplus of exporting lots of goods.