The post-colonial age refers to the period since 1945, when numerous colonies and possessions of major Western countries began to gain independence, in the wake of the end of World War II.
The process of decolonization has occurred all throughout modern history of the Western world; namely any time a colonial possession achieves independence or sovereignty, or some form of greater autonomy, that is a valid occurrence of decolonization; however the period since 1945 is particularly notable, largely due to the breakup of colonial empires held by many major European powers.
The period following World War I was somewhat parallel, since it involved the breakup of the colonial empires previously held by the nations which were the losing side in that conflict. However, the period after 1945 was highly notable and arguably unique, since it involved the breakup of colonial possessions of virtually all European powers, including very much the nations who had been the victors in World War II.