There's a variety of types of popularity. It depends so much on context, the other people in the group etc. Some people may be very popular in one place but not in another.
Popular types I have known...
Bullies
At school the "popular" people were often the most badly-behaved, spiteful ones who had a crowd of followers. The nice, quiet, studious people were the ones who got bullied for being "square" and were less likely to be particularly popular.
Charmers
The ones who know how to put on the charm, even if it's not sincere. Usually physically attractive. May fit the following description:
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They know how to make others feel good in order to get what they want. They'll appear oh-so-charming to most people, but if they meet a possible competitor they'll cut them out and undermine them behind their back. They often get away with it.
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You can spot them by the wide smile they flash at people... it disappears immediately once the other person has walked past, instead of fading gradually as a real smile would.
Charismatic Leaders
May be genuinely inspirational, honest, innovative etc. and able to direct forward a great idea, product, philosophy etc. Popular because they really are capable, likeable, reliable, someone people aspire to be like.
But some charismatic leaders (televangelists, fundamentalists, politicians) may be popular purely because they're believable, regardless of the unpalatability of their actual message.
Includers
Someone who puts other people at their ease, isn't cliquey, makes people feel good about themselves by taking a genuine interest in others.