A more thorough explanation:

Eignesse (ay-nes), n. [French] refers to esnecy (es-ni-see), which means seniority. It is the condition, right, or privilege of the eldest-born. This term is especially used to describe the privilege of the eldest among coparceners to make a first choice of shares upon a voluntary partition. It is also known as aesnecia.

For example, if a father has three sons and he dies without leaving a will, the eldest son will have the right to inherit the property first. This is because he has the privilege of eignesse or esnecy.

Another example is when a family decides to divide their property among themselves. The eldest member of the family has the right to choose their share first, according to the principle of eignesse.

These examples illustrate how eignesse or esnecy refers to the right of the eldest-born to have priority in certain situations, such as inheritance or property division.