To keep it as simple as possible, there are two main types of bulletproof vests; soft and hard.
Soft vests are made of woven kevlar. These are tiny strands of extremely strong fabric. They’re woven and layered up to create a relatively soft, flexible panel.
This stops bullets by slowing them down as they impact the kevlar, losing energy as they rip through the layers of fabric.
Think of it like a speeding car plowing into a bunch of buckets filled with water.
These soft vests are the type typically worn by police. They’re designed to stop most handgun rounds.
The second type of bulletproof vest is hard armor. This is typically in the form of steel or ceramic plates.
Basically these are just strong enough to withstand the impact of a bullet. Ceramic plates shatter and spread out the force of the impact much like kevlar does, but on a higher level.
These type of vests are worn by military. They’re designed to stop rifle rounds. Increasingly, police will carry these in their cars as well.