What they are for:
These caps have an adjuster in their center which pushes on the fork spring so you can adjust your bike's ride height, technically, "sag", without having to disassemble the fork to add or remove spacers. Sag/ride height is the point, not fork feel, though that is important also. See this resource for more on the importance of setting up your bike's sag.

If replacing air type fork caps, the benefit of these new adjustable caps in that case is more that now you will adjust ride height mechanically instead of with air pressure, freeing up your fork to be more supple and less jerky.

Installing:
Use well-fitting, preferably 6-point, sockets on these soft aluminum parts to avoid tearing them up. Oil or grease the threads, inside and out, on your new caps. Grease the two sealing o-rings (small one on the adjuster, large one on the cap body) also.

If your bike has very small diameter fork springs, you may need to replace the jiffy type cotter pins at the bottoms of the new adjustable fork caps with standard cotter pins.

Obviously, you need the front end off the floor before you can install the caps. In most cases you will need to modify or replace whatever fork spring spacers (tubing) is at the top of the fork spring right now. The new caps are slightly longer than the original, so if keeping the same springs, you will need slightly shorter spacers. See the next item.

Using:
Although it is possible to adjust the caps with the bike fully planted on the floor, it is not best practice and will likely result in breakage of the adjusters. Ideally, make sure the front end is off the floor before you turn the adjusters. They have aluminum threads after all, so you don't want to try to turn them against hundreds of pounds of force.

If you find that the available range of adjustability isn't resulting in the ride height you want, then you need to either shorten or lengthen the spring spacers inside the fork.

Fitting on former air-assist forks:
If your fork had air caps previously, you will need to experiment a little more than you would otherwise, to find the optimum combination of spring spacer and cap adjuster setting to achieve the same result the compressed air was providing before, to the degree that you were depending significantly on air pressure previously.