Thomson scattering is a type of scattering of photons by free charged particles (e.g., electrons) in which the outgoing photon has the same frequency/wavelength as the incoming photon, i.e., a type of elastic scattering. It happens when the photon energy is much less than the mass energy of the particle, and is the low-energy limit of Compton scattering. It tends to polarize the electromagnetic radiation.
In discussion of radiative transfer, Thomson scattering and the higher-energy analog, Compton scattering are referred to as electron scattering, because an electron's direction is changed, i.e., it is scattered, and/or because it causes a photon's direction to change, i.e., it scatters the photon.
Thomson scattering is an element in the physics of stars. Similarly, it affected the cosmic microwave background as a polarizing influence when the electron density of the universe was high enough to significantly scatter the photons (i.e., before and during the epoch of reionization).