The phrase "major centres" refers to important or significant places where a lot of activities or services take place. These centres are usually bigger or more prominent than other places. Full definition
They weren't sure about accepting: it would mean striking out alone, in a small university in a country isolated from the world's major centres of research. (scientificamerican.com)
Flights are affordable and frequent with efficient connections between major centres. (holidayextras.co.uk)
While homes in big cities may sell quickly, outside major centres homes can sit on the market for months and months. (moneysense.ca)