Quote Currency
Also called the "counter currency" or "price currency," the quote currency sits on the right side of the slash in any currency pair. The number you see as the exchange rate is denominated entirely in the quote currency. In USD/JPY, the Japanese yen is the quote currency, so the rate tells you how many yen one US dollar buys — for example, suppose the rate is 150.00, meaning one dollar fetches 150 yen.
A rise in the pair's price always means the base currency has strengthened relative to the quote currency, and therefore the quote currency has weakened. This is the part that trips people up: if USD/JPY climbs, the dollar is getting stronger and the yen is getting weaker, even though the yen is the one that appears to be increasing in number.
The quote currency also determines what currency a profit or loss is initially settled in for anyone tracking a position in that pair — a detail that becomes important when comparing returns across different pairs. For a fuller picture of how exchange rates are constructed and what moves them, see the what moves exchange rates guide and the live currencies page.