What is meant by "taking the concession out of necessity"? Is the necessity religious or worldly, or both? And is adopting Abu Hanifa's view on marriage without a guardian considered taking the concession out of necessity?

A Sharia (definition) dispensation is what has been legislated contrary to the original ruling to alleviate hardship. Adopting the dispensations of jurists means that a responsible individual acts upon a ruling that offers them alleviation and removes difficulty when there is a need.

Need is a category between necessity and enhancement. It provides expansion and removes constriction from the responsible individual. It includes religious needs (such as fear of zina) and physical needs (such as fear of physical harm resulting from the retention of excess).

It is permissible to adopt the view of Abu Hanifa, may Allah have mercy on him, regarding the marriage of a mature woman without a guardian when there is a need, subject to conditions and controls. These include: that the opinions are religiously recognized and not anomalous; that there is a genuine need to alleviate hardship; that the one adopting it is qualified to choose; that it does not lead to impermissible concoction or falling into an illicit objective; and that the person seeking the dispensation feels at ease. Concoction is impermissible if it leads to adopting dispensations merely out of whim, or to violating controls, or to overturning a judicial ruling, or to overturning what was acted upon through imitation, or to contradicting consensus, or if it leads to a complex situation that none of the mujtahids would endorse.