on the eclipse the dual mono means that you can plug 2 separate inputs into 2 different fx and output them on 2 different outputs. So the left in feeds one effect which outputs only on the left output. same with the right.
Dual Mode can take 2 different inputs into 2 different fx and sum them on the stereo bus.
then you have parallel and serial modes which take one input into multiple processors. the parallel mode adds the dry signal into each individual processor then sums them together on the stereo bus. Serial daisy chains the fx.
I think most of the time you would want to be in serial mode unless you were trying to do some special processing.