Briefly, in conventional (diffusion flame) combustors, as saludos says, the fuel/air mixture in the primary zone, where the fuel is burnt, is heterogeneous or stratified. Therefore the fuel/air ratio varies a great deal from lean to near stoichiometric. Thus high flame temperatures result in the regions where the fuel/air ratio is near stoichiometric, i.e. equivalence ratio, which is the fuel/air ratio to the stoichiometric fuel/air ratio, is nearly unity. This results in high flame temperatures, hence NOx emissions. In premixed systems, we thoroughly mix the fuel and air prior to combustion such that the equivalence ratio is in any part of the fuel air mixture never greater than 0.6. This results in low flame temperatures and therefore NOx emissions.
To achieve all this in a single stage of combustion is difficult because at low loads the equivalence ratio will decrease below the weak/lean extinction limit and the engine will flame out, particularly in aero derived gas turbines or gas turbines operating with a free power turbine. We therefore split the combustion process into two or more parts (staged combustion) and vary the fuel flow to each of these stages in a controlled manner as the load is reduced. These types of combustion systems are often referred to dry low emissions or NOx combustion systems (DLE/DLN). You can learn more about such gas turbine combustion system and gas turbine combustion is general by reading Gas Turbine Combustion by Lefebvre.
Regards,
gtsim