Why is there more water in the zone of saturation than in the zone of aeration?

In zone of saturation it already starts to rain (100% saturation).

I guess you are talking about phreatic (free) underground water.

Rock/soil is made of a matrix (sand/clay/limestone etc...) and pores (empty spaces like the space between sand grains). In the zone of aeration (vadose zone), the pores are not filled fully with water but contain still air. This zone is comprized between the ground level and the top of the zone of saturation.

In the zone of saturation, the water fills all the pore of the rock. Between the vadose zone and the zone of saturation, there is the capillary fringe were the water of the zone of saturation is kind of 'sucked' by the thinest pore by a force called capillary pressure. To illustrate capillary force, take 2 rectangles of translucent plastic or glass. Put them in a glass, half in, half out. Then bring then nearer and nearer to each other. When they will be about 1/2 to 1 mm of each other, the water will be climbing between them. I hope you understand me...