I'll add a little to CM1995's response for those not totally familiar with how to get proper compaction.
First and foremost there has to be a proper amount of moisture for the material being compacted. This varies by soil type, where exact moisture content is more critical in some soils and not so in others. A real crude field test that works pretty well for a lot of soil types is as follows: make a ball out of the material by packing it with your hands (much like making a snowball). Then drop the ball from about waist high on hard ground. If the moisture is proper it will break into a few large pieces. It it doesn't break at all, it is too wet. If it shatters into many small pieces, it is too dry. I know it is a crude test, but it is surprising how well it works on a variety of soils. Of course it is not scientific and doesn't apply equally to all soil types.
Secondly, you have to have 2 of the following present to get good compaction: pressure, kneading, impaction, and vibration.
Some for instances:
Skid steer has kneading from the lugs on the tires and pressure from the weight
Dozer has kneading from grousers and vibration from the tracks (although the dozers can be heavy, the pressure per square foot is small with tracked vehicles)
Vibrating rollers have vibration and pressure
You can get compaction from one of the four above by itself, but it usually is just surface compaction and doesn't penetrate as deeply as it would if another form was also present. For instance, in the dump truck example, you have mostly pressure with a small amount of kneading depending upon the tire type.
The amount of lift you can compact depends upon how much of the four factors are present and to what degree. For example, a skid steer and a 5 yard loader are similar in design and both compact using kneading and pressure. The 5 yard loader, because if its size and lbs/sq. foot pressure can compact larger lifts than a skid steer. Both would do a better job of compacting if their buckets were full vs. empty.
Like most things in the dirt world, experience is the best teacher. The more soil types you encounter and the more different equipment you use, the better you get at selecting proper equipment, maintaing proper moisture, and determining proper lift height for any soil type to get good compaction.