There are primarily two types of transmitter modes available for RC radios. The difference between mode 1 and mode 2 is where the throttle and elevator controls are positioned on the transmitter.
With Mode 1, the right stick controls the ailerons and the throttle. The left stick controls the rudder and elevator.
With Mode 2, the right stick controls the ailerons and the elevator. The left stick controls the rudder and the throttle.
The throttle stick is the only stick that does not spring back to neutral position when letting go of the sticks. This makes it impossible to switch from mode 1 to mode 2 without taking the radio apart and switching around the mechanical components.
I don't know about you, but I'd rather not take the chance of destroying a $200+ transmitter. So be sure to choose the right mode when purchasing your radio.
One mode is not necessarily better than the other. The best thing to do is to choose the mode that most of your peers and/or instructor use.
Most pilots in North American use Mode 2 transmitters. If you order a transmitter without specifying the mode, you will receive a mode 2 controller in the U.S.
Most locations outside of the U.S. use mode 1 transmitters. But there are no official rules or standards anywhere that I know of.
Heck, I live in the US and there is a guy at our club that uses Mode 1. And he's a darn good pilot too!
Do some research and find out what others are using before you buy your radio. This is especially important if you live outside the U.S.