Simply put, and to the best of my knowledge, they are different channel configurations, usually (again to the best of my knowledge) based on varying preferences in the r/c flying community. In other words, by switching modes you switch which stick or other control on the t/x will be connected to which r/x output.
From a boating perspective other modes than Mode 1 can at least on certain sets be of some interest because they no longer assign the throttle to left stick up-and-down, thereby removing the aeroplane-based set-up for that stick that full down = no throttle.
On my Spektrum set, in Mode 1 a rather irritating alarm would sound if I turned the t/x on with the throttle set to mid-point (the boater's neutral), because the thing assumed that an aeroplane engine was about to be turned on at mid throttle (something that could indeed be a rather bad idea, and worthwhile warning the user against) as soon as the r/x was also swtiched on.
By switching to Mode 2 (I think it was, or it might have been Mode 3 or 4; can't remember off the top of my head), this problem went away, because the throttle channel was no longer assigned to the left stick up-and-down. I still use this stick for throttle, mind you, but I plug the ESC into another socket on the r/x, namely the one assigned to the left hand stick up-and-down in Mode 2 (again can't remember which r/x output that happened to be, but it doesn't really matter). If the manual for your set does not tell you how the modes are configured, you can find out easily enough by simply connecting a servo to each r/x output socket in turn and noting down wich stick or other control makes it move in each output.
/Mattias
Edited By Banjoman on 08/12/2014 12:09:59
Edited By Banjoman on 08/12/2014 12:13:36