To put it simply, a high emissivity object is better able to radiate energy than a low emissivity object.
A blackbody would have an emissivity of 1, meaning that it would emit 100% efficiently.
Lower emissivity objects would be less efficient emitters. An object with an emissivity of 0.6 would emit 60% of the energy that a blackbody would under the same conditions.
The image above is a small piece of polished metal with a piece of PVC tape stuck at each end. The tape has an emissivity of 0.95, so it is a good emitter and emits energy well. The polished metal has a low emissivity and does not emit as well.