Currency pairs quote how much of the second currency one unit of the first buys. EURUSD at 1.09 means one euro buys 1.09 dollars, and the pair rising means the euro strengthened, or equivalently the dollar weakened.
For an investor holding foreign assets the exchange rate is a second, uncorrelated source of return. A European stock that gains eight per cent in euros while the euro falls six per cent against the dollar has returned about two per cent to a dollar-based holder.
Rate differentials drive most major currency moves. Capital flows towards the currency offering the higher real return, which is why foreign exchange markets react to central bank language as sharply as bond markets do.