Final answer:
The distinguishing feature of a prostitute is the eagerness with which she offers herself for hire to men.
Step-by-step explanation:
The feature that distinguishes a prostitute from other women who engage in illicit sexual intercourse is the eagerness with which she offers herself to men for hire.
In the given text, it mentions that the word 'openly' refers to a woman who engages in sexual activities without choice, sustaining the role of a prostitute. It is important to note that prostitution involves exchanging money for sexual services in a professional capacity, distinguishing it from adultery or fornication.
Therefore, the correct answer is Eagerness (B).