The phrase "to hug the road" means to drive or steer a vehicle closely and securely along the road, usually to maintain control and stay in the correct lane. Full definition
Interestingly they're also promising «stunning visuals and car physics that hug the road even at top speeds all built around a gripping storyline.». (wolfsgamingblog.com)
Audi magnetic ride can be adjusted to three settings (comfort — auto — dynamic) via Audi drive select and, at the press of a button, either makes the compact sports car hug the road more tightly or lets it glide smoothly across the road irrespective of which mode the driver selects. (greencarcongress.com)