First of all, let us not think that human trafficking is only a modern phenomenon. After all, there was a huge trade in African slaves for centuries in the past. That said, modern human trafficking is caused largely by the disparities in wealth between rich and poor countries and even between rich and poor within various poor countries. This disparity means that there are people poor enough to consent to have (for example) their children trafficked while there are, at the same time, many people rich enough to buy the trafficked people or their services.
In my answer to your other question, I spoke of the sex trade in Thailand. This is an example of the points made in the previous paragraph. There are multitudes of poor people all over Southeast Asia. Some will be willing to sell children to be trafficked simply because they cannot afford to support the children. Alternately, there are many who are desperate for work and accept offers that turn out to be fronts for trafficking. Such trafficking is used to procure sex workers but also to force people to work in industries such as food processing. At the same time that there is such poverty, there are many people in Thailand and abroad who are rich enough to take advantge of trafficked people. People come to Thailand from around the world to patronize brothels.
This, then, is an issue of supply and demand. There are so many poor people that there is a supply of people to be trafficked. At the same time, there are so many rich (and unethical) people that there is a demand for trafficking. This is why there is so much human trafficking today.