Suburban refers to areas just beyond a city’s border. Your parents might have grown up in the city and then moved to a more suburban area after they had kids.
If you see a lot of malls, plus houses that all look the same, and you're just outside a city, then you're in a suburban area: the suburbs. If you're from the suburbs, the chaos of New York City might be shocking. Suburban areas aren't as busy as urban (city) areas, but there's a lot more going on than in rural areas — farmland. One difference between suburban and urban areas is the urban areas have more cabs and public transportation.