Explain why the colombian government agreed to extradite drug traffickers to the us for trial during the 1980s.

In the 1980's (and still today to some extent) the drug cartels the boss in Columbia. For example, the Cali Cartel was able to bribe law enforcement officials in Columbia to avoid prosecution. They ran wiretaps on the government to know when they were getting close to being caught, which is incredibly impressive since it's hard for other governments to wiretap the law enforcement divisions of another country. The cartel had zero fear of being prosecuted in a Columbian court because it was very likely that they had not only bribed the judge- but also the official that selects the judge for cases. The Cali Cartel was far from the only drug cartel in Columbia that existed with the aforementioned capabilities; though it certainly was the most prolific. 

Basically, the Columbian government had lost control of the situation and no longer possessed the ability to contain any of the cartel's criminal activity. Luckily for the citizens of Columbia, the government was able to recognise/admit this, which was the main (and pretty much only) rationale for the Columbian government setting up the extradition treaty that they did with the US.
The Treaty was actually very successful and is widely considered to be the worst threat to face the cartels at the time. Some of the cartels did attempt to influence the trials that went on in the US, but very few had any success, and the ones that did weren't able to do enough to sway verdicts. Even though the government could extradite any Columbian citizen that it suspected of drug trafficking, meaning that they didn't require conclusive evidence (just circumstantial evidence), almost all of the trials that took place in the US ended in a prosecution of some sort. 

The treaty reached peak success during the time that it was supported by the then Columbian Justice Minister Rodrigo Lara Bonilla, and during this period of time, the treaty forced all of the major cartel drug lords into hiding out of Columbia. 

Hope that answers your question, it's a little bit longer than what most people are looking for on this site, but you have to know a fair amount about the situation to really understand IMO. Cheers!

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Magma is outside the volcano  and lava is inside the volcano.