A term used in the United States referring to a place in a large city that is mostly populated by poor minorities. It has nothing to do with the actual inner part of a city, and generally refers to a wedge-shaped area within the city limits that separates the downtown area from the suburbs, such as the Bronx in NYC, the South and West Sides of Chicago, Dorchester and Roxbury in Boston, and South Central Los Angeles.
The inner part of a city is the downtown area, but the part that is called "inner city" is the outside part.
Almost always used to describe poor minorities living near a city. This doesn't actually mean they live IN a city. Plenty of people live in a city, but would never be described as "inner city."
The inner-city schools are struggling to keep up with the rest of the nation.