Turning radius is the amount of space required for a car to make a complete circle at full steering lock in either direction,
It affects maneuverability
A car with large turning radius even if it's smaller requires more space for maneuvers than a larger vehicle with smaller turning radius
E.g. 9th generation Corolla (2002-2007) and 5th generation honda city (2009-2021) both have almost same dimensions externally (city being slightly longer, corolla being slighlty wider) but when making a u turn or parking in a tight space the city is easier to maneuver,
Older cars like mehran, khyber, cultus, older 90s city, civic and corolla had large turning radius means a u turn, tight parallel parking that wagon r, japanese kei cars can do quite easily in "one go", while a mehran, khyber, cultus one has to reverse and forward because the car can't turn as tight, requires more space for the same maneuvor.
And because newer generation vehicles have good (smaller or same) turning radius as older generation vehicles that's why u can see despite current compact sedans outgrowing 90s mid size sedans in external dimensions they still can be driven in tight streets and turns with much ease compared to older, smaller (compared to current compact sedans) midsize sedans.