In
particle physics, one usually does
scattering experiments to get information on, well, particles.
The earliest such experiment was done by
Rutherford, and I will attempt to use it to illustrate what the form factor means. Rutherford looked at the collision of
alpha particles with gold atoms. From the angular distribution of the scattered alphas he was able to deduce that gold atoms (and all others as well) consist of mainly empty space, and all the mass is concentrated in a small, hard
nucleus.
He did the math and calculated the so called
Rutherford cross section. He was right only by accident because he didn't take into account relativistic or quantum effects, but nevertheless his formula is valid for
spin-less, pointlike targets.
It turns out that the
cross section in a more general case can be expressed as the Rutherford cross section (with small modifications, see
Mott cross section) times a function F(Q^2) called the
form factor, where Q is the momentum transferred in the collision. This function is the
Fourier transform of the charge distribution of the target. In Rutherford's case F was a constant and as such did not distort his calculation. This is consistent with his idea of a pointlike nucleus - it gives a
delta function as charge distribution and the Fourier transform of a delta function is constant.
However, nowadays we have access to higher energy probes, and thus can do measurements with higher momentum transfers. Therefore we know that F is constant only for small values of Q^2, and nuclei are not points but have a substructure, namely
protons and
neutrons. The
nucleons themselves are also no point particles but consist of
quarks. The
Rosenbluth formula describes how their form factors relate to the cross section.