To find the difference between appreciation and depreciation of a currency, let's start with how they are alike. Both appreciation and depreciation measure the value of one or more currencies against one or more other currencies.
The value of things can rise or fall. A rise in value is called appreciation. An example of appreciation in the value of something is how a Rembrandt oil painting is worth more and more every decade (or even every year).
A fall in value is called depreciation. An example of depreciation in the value of something is how your 2015 Toyota Camry Hybrid ceases to be worth $29,000 once you sign the papers and drive it off the lot (the value of new car falls as soon as the new owner drives away with it).
To turn again to a nation's currency, appreciation is when the currency rises in value and depreciation is when the currency falls in value. But currency is a special case in rising and falling value. Currency valuation (measure of currency value) must be in comparison to another (one or more than one) nation's currency, for example, the US currency (USD) valuation may be in comparison with British currency (GBP).
To give an illustration of the concept of comparison appreciation and depreciation, a Rembrandt's value is not set in comparison to a Monet's value. A Rembrandt (and a Monet) have intrinsic value: the value rises or falls based upon the importance a Rembrandt (or a Monet) has in civilization. This is different from the valuation of currency.
Because most of the world's currency is not affixed to either a gold or silver standard measurement of valuation (there is no gold or silver in our depositories that can be given in exchange for every dollar held by every citizen or foreign currency investor, though there used to be). The world's currencies are on a floating exchange rate system, meaning that currencies develop value, or have value affixed to them, in comparison to other currencies.
To illustrate this concept, imagine that Japan is having steep inflation and its economy and currency are weak, indicating the purchasing power is less than it would be without inflation. Imagine that for import/export transactions and currency trading transactions, buyers and sellers (of import/export goods or of different nations' currencies) need to know what different currencies are worth in order to fairly complete transactions between nations with unlike currencies.
Now imagine that the United Kingdom's currency is strong and that they have a strong gross national product (GNP). If Japan and the UK had currencies with the same purchasing power, they could accept parity in valuation and make straight-across transactions. But when one currency is weaker (or stronger, depending on which side of the transaction you are looking at), then the weaker currency must be revalued to get an accurate trading value. In this hypothetical example, Japan's currency would be devaluated, or depreciated, in comparison to the UK's currency in order to facilitate fair buying and selling transactions.
Appreciation works the same way but in the opposite direction. If a low value currency has an increased capital inflow or an increased GNP, then that country's currency will become stronger, with an increased purchasing power, and will be upwardly revaluated, or appreciated, in comparison to the currencies of their trading partner countries in order to facilitate fair buying and selling transactions.
If currencies were on a gold or silver standard, then the appreciation and depreciation of currencies would depend upon the rising or falling price of gold as it became more or less scarce, but in a currency market based upon a floating exchange rate system (not fixed to a standard of valuation measurement), the valuation comparison is between the currencies of different countries, and the valuations of countries' currencies can vary depending upon how well or badly the country's economy is doing in terms of factors such as inflation, cash inflows, trade deficits, general economic fundamentals, political stability, general investment risk aversion and interest rates.