Transmitter modes are the setups for which stick controls what movement on the aircraft. Mode 2 is by far the most commonly used in the USA. In mode 2, the throttle and yaw (rudder) are on the left stick, the pitch and roll are on the right stick (elevator/ailerons). Mode 1 transmitters put throttle on the right stick, and I think roll (aileron) but not positive. There are also Modes 3 and 4, which mix the controls up differently. Mode 3 is a precise reversal of Mode 2, and Mode 4 is a precise reversal of Mode 1.
If you want confusion and disaster, try flying in a different mode than the one you are familiar with. As usual, don't ask me how I know!