Currency depreciation is the opposite of currency appreciation. It is the decrease in the value of one currency against another.
If the EUR/GBP exchange rate falls from 0.95 to 0.92 the British pound (GBP) has depreciated by £0.03.
One euro now costs £0.92 pounds (or 92 pence) instead of £0.95.
If a central bank cuts interest rates, assets denominated in that currency will be less attractive to investors as the interest they yield will be lower.
Consequently, the announcement of an interest rate cut normally triggers a depreciation of the currency, as investors tend to sell assets in that currency and buy assets in currencies with higher yields before the actual interest rate cut takes place.
Essentially, a currency depreciates because of a loss of investor confidence. Extreme losses of confidence can have a severe effect on a currency and by extension, the economic health of the country where the currency is used.