Many, many factors

There are many factors related to the birthrates and deathrates of many countries' populations. As Joanne had explained before about the factors, I will go more in depth about them so that everyone can understand better. The FIRST FACTOR is Lack Of Education. In developing countries like Africa and China, many people lack education. Because of this, many things happen that results in the increase of birthrate:
Lack of family planning skills and knowledge
-moreover, unaware about Sexual Transmitted Diseases like HIV/Aids
-not using contraceptives such as condoms and birthcontrol pills
-cannot control pregnancies
Not skilled, hence unable to hold proper jobs
-women do not have careers and stays at home only to cook, clean and sew
Early marriage
-many young women, like when they reach the age of 15-17, they marry. This is due to the fertility of younger women, more babies could be produced from younger women basically

SECOND FACTOR IS ABOUT TRADITIONS:
In less developed countries, farmers are common occupations throughout the country
-hence, farmers need a lot of manpower as plowing the field along with other works needs lots of labour (encourages high birthrate in the family)
Many still have preference for sons in the family (Gender discrimination)
-therefore, many family give birth to many children just to have a family heir

Next, deathrate is also high in less developed countries:
-they have lack of access to medical facilities:
1. they cannot afford for the medical treatment
2. some people in less developed countries do not have education, hence unaware of the consequences of the diseases in their bodies
3. medical infrastructure such as hospitals and clinics are limited in countries like Africa
4. medicines and vaccinations are limited in the medical industry

-lack of hygeine
1. no proper sewage disposal (bacteria that pollutes the water that they drink and infects their wounds)
2. poor sanitation (toilets)

-Malnutrition
-some people in less developed countries just have enough food to fill their stomach but the food is not nutritious enough (weak immunity)

For the developed countries, all the factors are towards the contrary.