Is it true that some international cities don’t allow vehicles to be driven every day?

Yes, that is indeed true. I think you are referring to the efforts some cities, such as Mexico City and Bogota, have made to reduce pollution (and in some cases congestion) by allowing vehicles with license plates ending in odd or even numbers to be driven on alternating days. Other cities have taken or are planning initiatives ranging from banning diesel and/or older vehicles that don’t meet current emissions guidelines (Seoul, Paris, London, etc.) to eliminating all vehicles from city centers (Oslo, Madrid).