This might be confusing at first but all there is to currency trading is exchanging your cash with another currency which you hope would increase in value against your former currency in the future. In stocks, looking at the quote for Microsoft corp. gives you 31.50 US Dollars per share, when you buy that stock you are exchanging your US dollar for shares of Microsoft (MSFT) we can re-write it as MSFT / USD. When the price of Microsoft increased to $32.00, that means the Dollar fell against stocks of Microsoft. You then trade those shares of MSFT and got more US dollars. Let's move on to another asset this time you're speculating on real estate. You found a house that is worth $400,000 and bought it in hopes that within a year, its value would increase, we write it down as House / USD. After a year you traded it and got more US dollars since the house would sell for $450,000. We could say that the US Dollar fell against your house since it takes more money to buy that house now than from a year ago.
This goes the same with currencies, but instead of buying those assets stated above, you buy another currency in which you hope would acquire more of your former currency once you traded it back in the future. Lets say you want to buy the British Pound, you look up the quote and its trading at $2 US dollars per pound. You then traded your $2 US Dollars in your pocket for 1 British Pound. Miraculously, after a year, you look up the quote for the British Pound and its at $3 US dollars per Pound. Obviously, the British Pound gained in value and you can now get more US Dollars with your single Pound.