Any current in electrical conductors generates a magnetic field; such current
is caused by voltage differences (i.e. an electric field). So, one can solve
for the current in a messy ground interconnection by knowing the nodes
that source and sink current, and setting up the interconnected equations
of field effects (such as inductance, resistance, capacitance) in the metal parts.
The picture shows only two layers of wiring, but a third (ground plane)
layer is implied by the labels.
A ground plane, and power planes, are intended to make such a detailed calculation unnecessary.
Inductance and resistance are both low when you use big pieces of copper; never
perfect, just good enough.
It's a sensible way to make high-performance circuitry, but you can make
more economical products with simple 'design rules' regarding trace
size, routing, and bypass capacitors for power and ground distribution.
The three-layer Arduino layout seems to be made using design rules with
wide traces and capacitors sprinkled about, but near to the expected
current nodes, in its power distribution. Wide traces take up
more space, but have lower electrical resistance and inductance than
narrow traces. Together with (a dozen) bypass capacitors, that can
keep all power deviations small enough to be ignored.