If a body has a positive temperature then it will emit radiation (over some very low limit perhaps).
Imagine a hollow sphere at a uniform temperature $T$. radiation will be emitted from the walls inside the sphere and absorbed by the same walls.
Consider a small part of this wall it loses energy by emission of radiation and gains energy by absorption of radiation from other parts of the wall. - Overall there is 'equilibrium' because all parts of the wall are at the same temperature and emit the same range of wavelengths with similar intensities.
What is this equilibrium all about?
as described above it is about exchange of energy between bodies of the same temperature.
Why is it important here??
Because if different parts of the system had different temperatures then they would emit different intensities/wavelengths of light - this would transfer energy from the hotter to the cooler body and mean that the spectrum of light was not 'blackbody radiation'
If there is thermal equilibrium, why does the body radiate??
All bodies will radiate photon unless they are really cold and very close to or at absolute zero temperature.