The term on the left-hand side is the mean kinetic energy. The individual gas particles (with mass m) follow a Maxwellian velocity distribution, resulting in a spread of velocities, v, about the average value. On the right hand side of the equation, T is the temperature of the gas and k the Stefan-Boltzmann constant.
Compared to a stationary observer, any particular atom, element or molecule could be moving along the line-of-sight, perpendicular to the line-of-sight, or some combination of both. This means that every spectral line emitted is Doppler shifted relative to the observer, resulting in a small change in the observed wavelength. This spreading of a spectral line due to the temperature of the emitting medium is called 'thermal Doppler broadening'.