You get to the crosswalk and wait at the intersection. You use the time to check your phone, so you actually don't notice when it switches to the walk symbol. By the time you look up, it's a red hand that is flashing. You look at the lights on the street going the same direction, and they're green. Now what?
Most people would just try to cross. After all, the lights going that way for the cars are still red. The flashing hand means that pedestrians haven't been instructed to stop crossing yet. Isn't it safe?
Despite how common this is, that's actually not the intent. You are only supposed to start crossing during the walking symbol itself. If the hand begins to flash after you start, you can keep going to the other side of the street. It's just warning you that it's going to change soon.
However, if you have not started crossing when the hand begins flashing, you are not supposed to start at that point. You don't know how long it has left unless there is a counter. You might not make it across. You're supposed to wait until the next cycle.
As noted, some crosswalks have a countdown. This can make it safer for people in the road because they know how long they have to finish crossing.
It's important to understand how this works so that you don't find yourself in the middle of the street as traffic begins moving. However, remember that even following the rules properly does not guarantee you won't get injured in an accident caused by a careless driver. If that happens, you may need compensation for your medical bills.