It means cities/metro areas.

Does it really? I would not have said so. I work as a consultant for a major international (I wont say who ) company and they only quote 190 or so "international markets"

They must be counting multiple markets per country. There aren't that many countries in the world and there are a significant number of countries where Uber doesn't operate all. As an example, afaik they no longer operate anywhere in south east Asia.

I don't think it's necessarily standard to use it that way, but it makes sense for Uber because their areas of operation (markets) are defined by cities (i.e. you can't just call an Uber in the middle of the country; it has to be within one of their operating cities).

Read this sentence as "600+ major markets, internationally".

A "major market" is basically a city/metro.