Yes, the name of the process to which you are referring is subinfeudation.
It's important to remember that most people only had a few meaningful things to trade - land, food, fighters, and protection. Feudalism is giving the people above you food and fighters and giving the people below you land and protection.
The King was at the top and granted rights to a lord, who would either work the land with his own peasants or through subinfeudation create another lord as middle tenant below him. That middle lord had his own vassals work the land, for which he paid duties (taxes) up to the chief lord. The middle lord could in many cases also subinfeudate. And of course, there were meaningful military obligations bound up with feudalism and vassalage. Wikipedia explains it well:
Below the king in the feudal pyramid was a tenant-in-chief (generally in the form of a baron or knight) who was a vassal of the king, and holding from him in turn was a mesne tenant (generally a knight, sometimes a baron, including tenants-in-chief in their capacity as holders of other fiefs) who held when sub-enfeoffed by the tenant-in-chief. Below the mesne tenant further mesne tenants could hold from each other in series. The obligations and corresponding rights between lord and vassal concerning the fief form the basis of the feudal relationship.
As a result, it became very meaningful to hold your land or status directly beneath only a King or Emperor. Your obligations and taxes were lesser and your prestige was greater. The Imperial Free Cities (mostly German cities under the Holy Roman Emperor) had no mesne lords and owed fealty directly to the Emperor, giving them autonomy to grow and prosper.
At least in early feudalism, the arrangement was that the vassals owed fealty and paid homage to their lords, including both taxes (often paid in kind with foodstuffs or other goods) and military service to the lords, and the lords would in return provide the vassals with military protection. To put it crudely, it's like a mafia protection racket. You pay powerful people to stay in business and they provide protection. Except that feudal vassals had to provide troops and weapons (commensurate with their ability to do so), which is not a parallel for the mafia protection racket.
Note that medieval vassalage was a complicated legacy system, not the product of prior design or comprehensive reform. So you get strange exceptions and situations, such as special rights for religious institutions, universities, cities, ports, and so on. You also have a complicated tree of duties and obligations, including the strange situation (well, strange to American notions of feudalism) that the English King was oftentimes a vassal of the French King.
Normandy in northern France was a duchy given to Norse invaders/settlers (basically Vikings) in the 10th century. In the 11th century their duke invaded England and is now known as William the Conqueror, the first Norman king of England. So for much of the next several centuries, the King of England was also Duke of Normandy, so a King in his own right and also a vassal to the French crown. In addition, the county of Anjou was held by Plantagenets, so Richard I Lionheart and his father Henry II were both English Kings and French vassals. This had relatively strange results, as when the Anglo-Norman kings fought the French crown they were going against the fealty and vassalage supposedly at the foundation of feudalism. Once again, the system was organic rather than designed.
But generally subinfeudation allowed for closer control over areas. Rather than the King directly monitoring hundreds, then thousands, and eventually tens of thousands of petit nobles, the feudal system allowed the King to deal with smaller numbers of more powerful lords and those powerful lords could more closely monitor a number of lands.
It was a way for the King to reward his followers with chief tenancies, and for his followers to reward their followers with mesne tenancies.