Cartagena got its name from the fact that it was a Carthaginian outpost during the days of the Roman Empire.  When Rome finally put an end to those pesky Carthaginians (241 BC), Cartagena became a Roman outpost/colony.  Every Roman city needs a theater so that Rome can maintain the Roman culture without being very in-your-face about it.  So the Romans built a theater in Cartagena, and you're looking at what's left of it.

When the Roman Empire collapsed near the end of the 5th century, Roman playwrights stopped sending new plays to the various Roman outposts — because there weren't any new plays to send.  Theaters throughout the Empire fell into disuse, and people forgot about them and/or repurposed them.  Cartagena filled theirs in with rubble so they could build houses atop it. 

Sometime in the 1980s, Cartagena's engineers were digging in the area and accidentally rediscovered the theater.  Existing plans were halted, and all hands bent to digging it out.  Parts of it were in excellent shape; other parts not so much, but it was preserved well enough that the curators could tell what it looked like when new, and there is a small section of the theater that has been reconstructed to its as-built condition.

It's a marvel.  Go see it.