As explained by Matt (Josh Brolin) to Kate (Emily Blunt), the purpose of the task force is to "take down" Mexican drug lord Fausto Alarcón. While this can be construed as "arrest and convict", the actual plan is to kill him, plain and simple.
The CIA's plan is that by weakening the Mexican cartels by such killings, the Colombian cartels can once again assume control of the drug trade in the americas. Their argument is that back when the Colombian cartels had a near-monopoly on the trade, there was a "semblance of order".
This period of time is referred to as "Medellín" in the movie, after the Colombian city and cartel of the same name. (Of course, the irony is that the United States did a lot to bring an end to the Medellín cartel in the first place.)
Since those "good old days", however, Mexican cartels have taken over, and the violence and chaos of the drug trade has both grown and moved much closer to the United States - and spilled over.
So, in essence, it's the CIA choosing to side with the devil they know. Like supporting a dictator or even overthrowing an existing regime, in order to provide "stability" from a U.S. point of view. Or, in this case, at least move the problem farther away.
There's also the characters' personal reasons for wanting Alarcón dead. Alejandro (Benicio del Toro) was a public prosecutor in Juárez, Mexico. His wife and daughter were killed (horrifically) by Alarcón's group. Since then, Alejandro has become a mercenary - or vigilante - in his attempt to get revenge.
As Matt explains, Alejandro will work for "anyone who will let him of the leash". That is, help him to kill the people responsible for the killing of his family. In this case, the ones letting him off the leash are the United States and, indirectly, the Colombian cartels. Hence why another character refers to Alejandro as "Medellín": He's doing their dirty work.