The bike headset is the hinge that allows the handlebars and front wheel to turn relative to the back wheel. There are two basic types. The new version is simple and light but - once set-up - doesn't allow much adjustment of the handlebar height. The old version is more complicated and heavier and requires special tools to adjust but usually allows more adustment of the handlebar height.
Old Type Threaded Steerer-tube
The old type of bike headset has an adjustable top race that sits just above the top of the head-tube. It screws up and down a thread cut in the steerer tube. It usually has hexagonal flats or a knurled ring. The nut above also screws up and down the steerer-tube and is used to lock the adjustable race in position. The handlebar-stem telescopes inside the steerer tube so can be adjusted up and down(link)
New Type Threadless Steerer-tube
On the new type of bike headset the steerer tube extends above the head-tube where it carries a stack of spacers and is topped by the handlebar-stem which clamps on the outside of the steerer tube and locks everything together. There are no flats on the top races of the bike headset as they don’t screw up and down, they are squeezed from above by the handlebar-stem.