Discernment is the ability to judge well. Merriam Webster breaks down discernment as discrimination, perception, penetration and acumen. The following is their description, which answers your question nicely. I have added a few words of my own.
DISCERNMENT “stresses accuracy in reading someone’s character or motives” and knowing whether his heart is in the right place. Always remember that actions speak louder than words. His actions will tell you everything you need to know. Is he reliable? Does he do what he says he is going to do? Is he respectful? Ask yourself these questions. If the answer is "No" then his character and motives are wrong.
DISCRIMINATION is the ability to “distinguish what is true or appropriate.” Do his words ring true? Does he say things that are off-color?
PERCEPTION implies “quick and often sympathetic discernment (as of shades of feeling).” For example, a discerning person would be able to see someone’s motives. Is he in it for fun or does he act like someone who cares?
PENETRATION implies a “searching mind that goes beyond what is obvious or superficial. Can you see the scorn beneath the friendly smile?” If you watch closely, sometimes you will see a flash of contempt, anger, or unbridled lust. Then his face will return to normal. If you see these things, beware.
ACUMEN is the ability “to see what is not evident to the average mind.” Some people have the gift of discernment. They just know. Others, like myself, have gained discernment through experience.
Someone who has no discernment is easily fooled, falls in love too fast, and has no idea whether he cares about her or not. That’s not a good place to be. But anyone can change that by paying attention and forcing themselves to be more aware. Mostly, listen to your gut. If he makes you feel sad more than he makes you feel happy, he’s the wrong guy for you or anyone. Get rid of him. You’re not his therapist.