Soil quality is a term that is hard to explain, but reflects an understanding of the usability of a given soil.
In most situations, the most important use of a soil is as to grow food, so the quality of a soil is understood as the ability to grow the highest yielding crops.
A soil can be impaired in a large number of different ways. This can include the effect of the soil texture and mineralogy, the amount of soil organic matter, the droughtiness (how susceptible it is to drought), the risk of flooding, the local climate and so on. Some of these factors are discussed here.
It may also be affected by the way it has been managed and be impaired by high levels of Soil erosion, high salinity/sodicity, pollution, etc. It may also have known susceptibility to specific plant pathogens which prevent growth of crops.
It may also be considered to be of low quality due to a range of local cultural and religious factors.
Hence it is only really possible to understand the term in a holistic multi-dimensional way, including soil properties, biology, chemistry and physics, previous management and local perception.
In simplest form, the Soil Science Society of America defines Soil Quality as “the capacity (of soil) to function”. Of course, the problem with this definition is that the ability of a soil to function changes depending on what you want it to do, and one soil which functions well as an agricultural soil may be poor at another function.
Generally speaking, the highest quality soils are used for the highest valued soil activities in a given area. There is usually some kind of pyramid of behaviour, with soils that are valued less being used for lower value activities, sometimes if they are not even particularly suitable for that purpose.
It is therefore entirely possible that the whole concept is bunk.
In contrast, soil and plant nutrients are well understood chemical ions which have a measurable effect on plants. So it is possible for a soil to be highly fertile (high in measured plant nutrients) whilst being low quality for other reasons. It is also possible for a soil which is low in nutrients to be considered to be relatively high quality.