It definitely doesn't mean "no motorized vehicles can ever travel in that area." There isn't one model, and in some medieval-era places there walkways which aren't exactly accessible with vehicles, but generally it means that pedestrians are given priority and private cars are banned or mostly banned.
There are many ways to exclude all or some private cars. Sometimes with a big sign and camera enforcement (this can be annoying!). Sometimes just by making it obvious cars aren't welcome in various ways. Sometimes with retractable bollards that can be opened with a code or a fob (you can, for example, allow taxis and local residents, but no others, this way).
It definitely doesn't mean "no ambulances allowed" and anyone who has seen an ambulance stuck behind cars on a jammed NYC street should understand how ridiculous the idea that pedestrians are an impediment to emergency vehicles is.
You can take public streets and allocate priority to various transport modes. There are always fights about those allocations and how best to achieve them, but this isn't a complicated problem. Like many things it is a solved problem that our big brained boys, operating only on vibes from behind their windshields, assume no one has ever thought about before.
Oh no how will the ambulances get in? Merde! We did not think of that!
This is Buchanan Street in Glasgow. Glasgow is hardly a pedestrian paradise, overall, but like most British cities it has some pedestrianized areas. If the police need to drive a car down this, they will! It isn't complicated.
Hey there's even a van in the picture!