That is what researchers said. What make them to say that? And based on what?
Before answering these questions we need to know three things: DNA, Y chromosome, and mtDNA.
We know that our body is made up of cells, and in fact our human body has about 100 trillions cells. In the center of each cell, nucleus, there are 23 paired chromosomes. Each pair chromosomes are half from father and other half from mother. The last paired chromosomes (23rd pair) are called sex chromosomes; XX is in female and XY is in male. Only male child carries Y chromosome from the father, and female child does not. Thus the father determines the sex of a child. Each chromosome is made up of a string of DNA (Deoxyribonucleic Acid), which is in turn made up of genes. Genes determine the traits (characters) of a person (heridity). One of the DNA functions is to pass that genetic information from parents to the child.

Besides having the nucleus in the center, each cell does have other different components; one of the components are mitochondria which provide energy to the cell. These mitochondria  also have their own DNA called mitochondrial DNA (mtDNA). Only mtDNA from the mother are passed to the child. The father's mtDNA got destroyed during fertilization. 

In summary we would say the following statements just for our subject purpose:

1. Chromosomes are made up of DNA, which determine the traits of a person. Those traits were passed from one generation to the next (from parents to child).

2. The Y chromosome is carried by male only. This means that Y chromosome is only passed from the father to his sons; thus I should carry my great, great, great, great, great,,,,, grand father's Y chromosome, and he could live some 60,000 years ago.

3. MtDNA is passed from mother to her child. The father's mtDNA got destroyed during fertilization; thus my whole family & I should carry our great, great, great, great,,,,,, grand mother's mtDNA, and she could live some 200,000 years ago.

Why do researchers believe that we, modern humans, originate from Africa?
Initially there were two suggestions about where modern humans come from. The 1st suggestion is that human ancestors dispersed throughout the globe, and modern humans evolved from these predecessors in various locations around the globe. The 2nd one is that all modern humans have the same ancestors, who emigrated from Africa some 60,000 years ago. After all data are analyzed, the latest suggestion appears to have advantage over the 1st one based on the following results:

1. Researchers have found fossils of modern humans in Africa, Australia, Europe, Asia, and America. From analyzing fossils, they conclude that fossils in Africa were older than the ones in other continents.

2. MtDNA testing had been done on some people alive around the world in 1987, and the result concluded that humans had mtDNA coming from the same woman who lived some 200,000 years ago in Africa. The fossils testing did confirm the finding that there were modern human fossils at that time frame in Africa. This means that woman was our great, great, great, great, great,,,,, grand mother. Scientists named her “Eve” or “Mitochondrial Eve”. Note that Eve here is not Eve in the christian bible.

3. Y chromosome - according to National Geographic researchers team, all living men have common male ancestor, who lived some 60,000 years ago. They named him “Adam”, and thus he is the great, great, great, great, great,,,,,,, grand father of all men alive today.

4. The current DNA testing (last year) on people alive today did confirm that we are all originated from Africa.

Why did our ancestors leave Africa some 60,000 years ago?
Nation Geography researchers team believe on some factors that make our ancestors left Africa. There was a super volcano eruption some 73,000 years ago in Lake Toba, Sumatra in Indonesia. It is believed to be the biggest one in 2 millions years and brought the global temperature down to frigid level in that winter. There was also the drought at the time. This drought and cold weather almost wiped out all populations, leaving only small surviving populations. Some of the surviving populations about 1,000 to 2,000 left Africa for other continents around 60,000 years ago. And here we are from thousands to several billions just in a period of 60,000 years.

Another factor they could leave Africa is because the sea level at the time was about 100 meters shallow than it is now. So people could cross continents with less difficulty.

Since we all originate from Africa why people are different? Why don't we look the same?
That is because of the evolution. People evolve to adapt to where they live. Researchers have found out recently why Africans skin is dark and Europeans skin is white. The answer to that question - our body needs vitamin D which is made from absorbing the sun ultraviolet light (UV); but the excess of UV light will destroy vitamin B folate (folic acid), and that is not good either. So people, living in sunlight area such as in equator, will have to do something about it. And they did; several genes were responsible to make the skin darker or lighter depending on amount of sunlight.  Those genes will make the skin dark enough to protect vitamin B and let the body absorb enough UV light to make vitamin D. People who live up north and down south of equator will have lighter skin because of the same reason. Those genes will adjust the color of the skin to lighter so that UV light is absorbed faster). The farther from equator is, the lighter the skin is. NASA has mapped the globe with the level of UV light, and the map matches the people skin. The higher UV light is, the darker the skin is.

Do you want to know your true line of your ancestors?
National Geography sponsors a program that you could join and know the line of your ancestors. What they do is sending you a package and request you to scrap your inside cheek with their sicker and send it back to them. The result will be available in few weeks, and it costs you only $100.