What is a Toroid used for and why does it need to be winded differently for different bands? Is it what generates the signals that get transmitted by the antenna?
Basically a circular inductor with a ferrite core instead of air which allows it to be more compact, have a higher inductance per volume and a greater q factor (bandwidth). A different inductance (different number of wire turns) is needed depending upon several factors, especially if you are using them to make a resonant circuit (a circuit that responds to a particular frequency). It does not generate the signal. I hope I got that right.
Adding to what some others have said, a toroidal shape for an inductor has some particularly nice properties for RF applications. The magnetic field outside an ideal toroid is exactly zero, regardless of what's going on inside the toroid. Even for real toroids, the leakage is very low.
Ferrite and powdered iron toroids are used for winding transformers and inductors. For radio stuff they are usually used as impedance transformers or as inductors in LC bandpass filters.