Chase This!
At times, women play hard to get as a screening device when they encounter more than one suitor.
It is commonly believed that the fun lies in the chase. The chaser can't stop obsessing over his chase, and constantly tries to be a part of his/her life. On the other hand, the person who (s)he is chasing also enjoys the attention. This comes across as cute and adorable in the earliest stage of a relationship.

This game is probably one of the oldest tricks in the book when it comes to dating. And like it says above, it is when one of the two prospective partners makes it harder for the other one by not giving them the time of the day.
Definition As Per the Cambridge Dictionary
"Play hard to get" means to pretend that you are less interested in someone than you really are as a way of making them more interested in you, especially at the start of a romantic relationship.
Understanding the Term with Examples
We often hear this idiom playing hard to get in terms of romantic endeavors. However, it can also be played into a formal context as well. On can play hard to get in terms of a new job as well.
In a Formal Situation
Example #1: Tom decided he would accept the job, but not before playing hard to get.
Example #2: Jane would have accepted the job position if it would be offered to her rather than playing hard to get.

Explanation: In both the above cases, Tom and Jane wish to accept the job. In the first the case, however, Tom has kept the job hanging in order to see what they or the other jobs can offer. Whereas, in Jane's case, she would take the job if it is given to her without a fuss.
In a Informal Situation
Example #1: Katey is very popular, perhaps because she plays hard to get.
Example #2: Why aren't you returning her calls? Are you playing hard to get?

Explanation:In these two examples, you can clearly see a similar pattern. One is being chased by another (of the opposite sex).
Now that you know the meaning of this idiom, let's move and see how it is put in use and what does it mean when a (wo)man is playing hard to get.
What Does it Mean When a Guy/Woman is Playing Hard to Get?
The gender rarely matters. This little game of cat and mouse is played by both the genders to pique the interest of the opposite sex. In a way, it makes the person feel wanted.

It is also a discrete way of keeping one person on the hook, while looking for other alternatives or simply not being easily attainable.

Under the facade of playing hard to get, the person who is being chased often does not return calls or texts. If it is a woman, she will not look over her shoulder and look at the guy or play with her hair while talking to him. But it will give him just enough flirtation to keep him from being disinterested.

However, if it is a guy or man, he will seem aloof and vague. Either way, the dance continues.
Such a small idiom, and so many interpretations. Chasing and being chased both might be fun, but if either is stretched for too long, it loses its interest entirely.