Qualified ownership is a type of ownership in which a person owns property, but their ownership of that property is conditional. This means that they do not have absolute ownership and complete control over the property; they only own it within certain parameters. These parameters are legally binding.
There are many different conditions that a person with qualified ownership of a property may be subject to. For example, a property may come with a permanent access easement that lets a neighbor pass through a property to reach their house. Or, a person may inherit land with the condition that it should never be sold to a mining or oil company.
The party who initially has absolute ownership of the land is typically the party who puts the conditions on the next owner's "qualified ownership."