It is my understanding that the title “Metropolitan” in the Eastern churches is similar to what we in the west would call an “Archbishop.”
Although in the Orthodox world, they do not have anyone higher up on the organizational flowchart (i.e. The Pope), so they probably assign more meaning and responsibility to the term Metropolitan.
In the Eastern Catholic churches, Metropolitans are the top bishops of their rites and many, like the Chaldean patriarch Emmanuel Delly in Iraq, are also Cardinals.
And I just want to let you know that I just went off the top of my head, and after reading what others wrote, I can say that my explanation likely contains many errors.