Some of the bigger players in the FX market include multinational corporations and investment institutions.
Say IBM wants to do business in Europe. They will need to make transactions in Euros. When they want to put those profits on the books they will need to exchange those Euros for dollars. Now they may only make that exchange a couple of times a year. So in the mean time they may hedge that exposure so they are not losing money to a depreciating exchange rate. This hedging will cause an imbalance in the supply/demand of the two currencies causing the market to adjust.
Investment institutions that buy bonds, for example, from another country will need to use the FX market to exchange their local currency for the currency of the country they are buying those bonds from. The capital inflow causes a supply/demand imbalance in the money supply of the two currencies causing one to rise vs the other.
Take last years bear market in the Euro as an example of investment institutions selling there European bonds (among other assets) because of the uncertainty of the Eurozones ability to repay their debt. They sold those assets in a local market receiving the local currency (Euros) in exchange. They then needed to exchange those Euros for their local currencies, say dollars for US institutions.
These are just to simplistic causes of exchange rate changes in a the complex FX market.