Good question! We need to think about what exactly it is that harms a passenger when a car crashes. The important thing to keep in mind is that when a car crashed, it goes from moving very fast to not moving at all very quickly: this means that there's a very large acceleration (acceleration is how quickly the speed of something changes). It's this acceleration that can hurt a human being.

During a car crash, a passenger without a seat belt will fly into the front of the car and stop suddenly; this sudden stop is where the large acceleration that hurts the passenger happens. The point of a seat belt is to "catch" the passenger and slow him or her down more slowly, decreasing the acceleration (this is also what airbags are for). Now, if a car is going REALLY fast, even the seat belt slows down the passenger too quickly, and can hurt the passenger.

You might ask: what does "REALLY fast" mean? Well, that depends on a bunch of stuff, like the type of car, the size of the passenger, the type of collision (head-on or side-on), and so on. For example, you may have heard that cars have "crumple zones" that are supposed to crumple in a car accident to decrease the acceleration on the passengers inside. Some cars have very good crumple zones and can protect passengers very well. In these cars, a seat belt is enough to protect a passenger in high-speed collisions. Other cars have smaller crumple zones, so in these cars, a passenger can be hurt by the seat belt even in lower-speed collisions

As you might have noticed, protecting passengers in a car can be quite complicated: that's why car companies put their cars through lots of crash testing to see how well a passenger is protected in an accident.