Magus Of Possibilities

Noble Phantasms represent the legends of a Heroic Spirit or in case of the lack of one it is what symbolize their existence, in other words, it can be anything technique, skills and etc

But first let me break down why exactly they are called noble phantasm noble implying the owner or the heroic spirit and phantasm implying mystery so as to say that it is the embodiment of the mystery surrounding the heroic spirit thus becoming their symbol that's also why legends shape how the noble phantasm will form

There are two main defining traits in noble phantasm legend and mystery

They are crystallized "mysteries",They are made using the imagination of humans as their core so that is where the legend part comes in then how it will be shaped is the mystery part referring to the process in the same way as humanity's illusions, they embody the ultimate mysteries of a hero as symbols of their existence through historical fact and anecdotes. 

It follows the Idol theory also called Idol Worship, is the term used to refer to the phenomenon wherein an imitation of a whole or parts of a subject, the source, gains properties and attributes that are inherent to that source which in this case is the legend.

It was taken to it's limits in Caster of Red of the Red Faction in Fate Apocrypha

As it can be anything Archer EMIYA's Reality Marble can technically be counted as one as it is the embodiment of his existence and mystery symbolizing his life which is the crystallization of his ideals

It is impossible for myths and legends to start from nothing, so they all have common points acting as the foundations that became the model for the legend. 

So it will explain why do Gilgamesh have the prototypes of the majority of the noble phantasms his legend played a part in that

To further solidify the point that it can be anything

There are cases where the nature of the Noble Phantasm is not actually a true crystallized mystery, such as Archer's Unlimited Blade Works, which is magecraft  although that magecraft is technically a mystery symbolizes him, and Li Shu Wen's No Second Strike, which is the quintessence of his martial arts which symbolizes the mystery of the technique he uses or it's pinnacle. Sasaki Kojiro is a case of a Servant without a Noble Phantasm due to his status as a wraith, but his technique, Tsubame Gaeshi that has solidified his legend , has managed to be on par with Noble Phantasms without the use of magecraft. Enkidu is described more as a "Noble Phantasm of the gods" than a Heroic Spirit, and Kingprotea is a being whose self can be treated as a Noble Phantasm.

The ultimate key point is that it symbolizes the said heroic spirit and the mystery surrounding the heroic spirit such as weapon, passive(example God Hand) or active skills (example Unlimited Blade Works or Phoebus Catastrophe), beings (example Belerephon), Treasures( example Gate of Babylon or Hanging Gardens of Babylon)

Note that they are different from personal skills and class skills in the sense that they are on the higher order in terms of mystery

There are further division on the classification of Noble Phantasms but I won't talk about them