Let us say - The domestic country is India where the domestic currency is Rs.
The foreign country America where the currency is USD. For Indians, USD is the foreign exchange.
Foreign Exchange like all commodities follow the simple rules of demand and supply.
Look at the following diagram :
X-axis: The Quantity of foreign exchange (supplied/demanded)
Y-axis: The Price of foreign exchange. This is given in terms of Rs - which is the Rs price of 1 dollar.
Initially, the market has a red demand and supply curves.
There is a an increase in Demand- demand curve shifts right to D1 (blue).
At the new equilibrium E1: the price of the dollar goes up from Rs 60 per dollar (E0) to Rs 70 per dollar (E1).
Now, this increase in price of Rs value of dollar represents a currency depreciation of Indian Rs. Earlier 60 Rs could buy one dollar but now you need 70 Rs to buy one dollar.
Or in Rs terms :
Earlier : 1 rs = (1/60) dollar , Now : 1 rs = (1/70) dollar
Hence the value of Rs has gone down - or the domestic currency has depreciated. This happens because when there is an increase in the demand for dollars, there are too many Rs chasing too few dollars in the forex market. Thus dollar appreciates and Rs depreciates.