I can explain from an economic geography perspective (bearing in mind the 20-year rule) with regard to Colombia.
First, a brief context!
Coca, the plant, originated in the Andes Mountains of South America and was revered by pre-Incan peoples. Leaves from the coca bush were used in religious ceremonies. At present, they are still used to combat debilitating effects of high altitudes.
In the mid-1970s, Colombian entrepreneurs began to export small quantities of cocaine to the United States. Very high profits allowed the exporters to become self-financing and expand. This allowed entrepreneurs to develop stable routes and links with coca paste suppliers from Bolivia and Peru. The suppliers created networks to acquire the chemical inputs necessary to refine cocaine and developed transportation systems to make large shipments and distribution networks, with a focus on markets in the United States.
By early 1980s, Colombia produced 11% of the world’s coca crop. During the late 1980s, Colombia had an economic growth of 4.5%, which was considerable when compared to other Latin American countries at that time. The industry has been said to be directly responsible with raising the standard of living of a million Colombians.
Basically, to be concise, you had four variables (probably many more), that led to the growth and spread of the drug trade in Colombia during the 1970s & 80s:
Historical and cultural use and cultivation of coca in the region.
Supply and demand (growing market in the USA).
Lack of agricultural alternatives. Many rural farmers, who had been living on subsistence crops such as corn, rice, and yucca, had switched to farming coca for various cartels or revolutionary insurgents. The farmers could not profit off their previous crops due due to poor infrastructure (getting the product to market) or regional strife. Thus, the ability to grow a product that had higher resell value and longer shelf life increased production.
Cartels and FARC: In Medellin there was a deterioration of the rapid industrialization of the city in the 1970s with various industries, such as textiles. This is theorized to have pushed more individuals into the informal economy (cartels) in order to survive. Additionally, political civil strife facilitated organizations, such as FARC, to begin selling cocaine as a means of income in order to purchase firearms, supplies, etc. Rural farmers, out of desperation, had (have) no other alternatives but to work for the various narcotics dealers and revolutionary groups.
I would suggest looking through the below readings.
Further readings
Thoumi, F. (2002) Illegal Drugs in Colombia: From Illegal Economic Boom to Social Crisis. The Annals, vol. 582, no. 1, pp. 102-116.
MacDonald, Scott B. (1989). Mountain High, White Avalanche: Cocaine and Power in the Andean States and Panama. The Center for Strategic and International Studies. Washington, D.C.
Mac Gregor, Felipe E. (1993). Coca and Cocaine: An Andean Perspective. Greenwoord Press. London.
Rensselaer Lee III. Dimensions of the South American Cocaine Industry. Journal of Interamerican Studies and World Affairs, Vol. 30, No. 2/3, Special Issue: Assessing the Americas' War on Drugs. (Summer - Autumn, 1988), pp. 87-103.