In general, each of the #ii is a Slot, which is an argument to a pure function. In your case, the three slots correspond to the three dimensions of the plot; so if you want to do something with the x values, you'd use #1. You wanted to use the real and imaginary parts, so that #2 and #3, respectively, because that's how you set up the plot. Abs[#2 + I*#3] is simply the absolute value of I^x since that's how you deconstructed the function values. (It's the same as Sqrt[#2^2+#3^2], if you'd rather spell it out.) The outer Abs just makes sure that positive and negative function values are treated the same way.

How about something like this? The curve is colored according to the ratio of the real part to the absolute value. This gives a balanced colouring, but you can play around with the ColorFunction more.

ParametricPlot3D[
 {{x, Re[I^x], Im[I^x]}}, {x, -4, 4},
 AxesLabel -> {"Real x", "Real y", "Imaginary y"},
 PlotRange -> All,
 ColorFunction -> (Blend[{Blue, Red}, Abs[#2/Abs[#2 + I*#3]]] &),
 ColorFunctionScaling -> False
 ]