“The population explosion” just means that the population increases rapidly.
The population, which used to be 1.5 billion in 1990, has been exploding to 7 billion. (as of Oct. 2011)
Three babies are born somewhere on the earth per second.
And now, 60% of the world population occupies the Asia, and the growth rate of population is high in developing countries especially in Africa.
Why does the population increase so rapidly? Let’s think about the process of the population explosion.

Like this, the population is finally to level off.
But, the population is increasing in developing countries. Because they need children.

Of course they want to hold in the population. But children are important labor in poor countries.
Also, as they can lose their children of tender years easily due to alimentary deficiency or illness, they have to bear much more children. So birth ratio doesn’t decrease, food supply doesn’t catch up with the population explosion.

So, the countries which can self-sufficient for themselves have balanced population.
The population cannot increase more than food production or food supply.