Some great answers already, so I haven't much to add. I can add some basic criteria from the DSM - 5.
The DSM lists about 9 different defining characteristics though I won't mention them all here. I'll outline a few which are quite interesting, and which might not have already been mentioned.
1. Narcissists are preoccupied and fantasise about wealth, status brilliance etc
2. There may be a tendency to possess a grandiose sense of self, there is a paradoxical 'ego' here where one possesses both a large and shallow ego.
Think of a narcissist's ego as being a large balloon, there is size but the balloon is easily punctured and creates a large bang when it does explode. So too, is the narcissist's ego, which is large but easily punctured, and when it does this can create violent results.
3. Along with this ego, of course, requires a sustained admiration from those around them as the DSM points out.
4. There may also be a heightened form of envy, or that others are envious of them.
These characteristics one might classify as ego maintaining carried to a pathological level.
The DSM notes that of those diagnosed with NPD, 50 - 75% are male.
'Narcissistic Personality Disorder' in DSM - 5 (pg. 669)
They see other less, they behave as if the world revolves around them. No matter what you do for them, they don't see it.
This is an impressive insight, thanks for the contribution @ayesha naymat
Superficially charming, lack of empathy, To support their fake charm and fantasy that they are superior their counterparts, Narcissistic person bullies them in order to have control over them.
They constantly need praise from others.